Instruction: Calculate Whole Life life insurance premium for 52 year old male, $750,000 coverage, Substandard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $750,000
• Duration: Lifetime Coverage
• Issue Age: 52
• Sex: Male
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_52): 0.005012
• Underwriting Multiplier: 1.5x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 90% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $7894.36
• Expense Charge: $1973.59
• Reserve Accumulation: $2631.45
• Profit Margin: $657.86
• Gross Annual Premium: $13157.27

PAYMENT OPTIONS:
• Annual: $13157.27
• Semi-Annual: $6841.78 (x2 = $13683.56/year)
• Quarterly: $3486.68 (x4 = $13946.71/year)
• Monthly: $1184.15 (x12 = $14209.85/year)

RESERVE CALCULATIONS:
• Net Level Premium: $9867.95
• First Year Reserve: $2631.45
• Terminal Reserve (Year 13): $360402.17

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Male
• Improvement Scale: MP-2019
• Select Period: 20 years
• Ultimate Mortality: CSO Male Ultimate

Internal Rate of Return: 10.9%
Profit Margin: 8.5%
Lapse Assumption: 6.6% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Whole Life life insurance premium for 52 year old male, $750,000 coverage, Substandard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $750,000
• Duration: Lifetime Coverage
• Issue Age: 52
• Sex: Male
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_52): 0.005012
• Underwriting Multiplier: 1.5x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 90% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $7894.36
• Expense Charge: $1973.59
• Reserve Accumulation: $2631.45
• Profit Margin: $657.86
• Gross Annual Premium: $13157.27

PAYMENT OPTIONS:
• Annual: $13157.27
• Semi-Annual: $6841.78 (x2 = $13683.56/year)
• Quarterly: $3486.68 (x4 = $13946.71/year)
• Monthly: $1184.15 (x12 = $14209.85/year)

RESERVE CALCULATIONS:
• Net Level Premium: $9867.95
• First Year Reserve: $2631.45
• Terminal Reserve (Year 13): $360402.17

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Male
• Improvement Scale: MP-2019
• Select Period: 20 years
• Ultimate Mortality: CSO Male Ultimate

Internal Rate of Return: 10.9%
Profit Margin: 8.5%
Lapse Assumption: 6.6% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate excess mortality during 2022 heat wave in Italy for Q1 2021

Response:
EXCESS MORTALITY ANALYSIS

Event: 2022 heat wave
Location: Italy
Period: Q1 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 75,153
• Observed Deaths: 81,027
• Excess Deaths: 5,874
• Excess Mortality Rate: 7.8%
• P-score: 7.8%
• Z-score: 3.10 (p < 0.001)

BASELINE CALCULATION:
• Method: Farrington surveillance
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.0% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 8.0% (587 deaths)
• 45-64 years: 7.7% (1,468 deaths)
• 65-74 years: 12.8% (1,468 deaths)
• 75+ years: 30.4% (2,349 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 3,161 (69%)
• Indirect (probable): 1,462 (19%)
• Collateral (delayed care): 871 (18%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [4,992, 6,755]
• Probability of chance: < 0.001
• Power: 0.96

Years of Life Lost: 81390
Economic Impact: $8.1 billion
Quality-Adjusted Life Years Lost: 57876

Human: Calculate excess mortality during 2022 heat wave in Italy for Q1 2021

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: 2022 heat wave
Location: Italy
Period: Q1 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 75,153
• Observed Deaths: 81,027
• Excess Deaths: 5,874
• Excess Mortality Rate: 7.8%
• P-score: 7.8%
• Z-score: 3.10 (p < 0.001)

BASELINE CALCULATION:
• Method: Farrington surveillance
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.0% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 8.0% (587 deaths)
• 45-64 years: 7.7% (1,468 deaths)
• 65-74 years: 12.8% (1,468 deaths)
• 75+ years: 30.4% (2,349 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 3,161 (69%)
• Indirect (probable): 1,462 (19%)
• Collateral (delayed care): 871 (18%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [4,992, 6,755]
• Probability of chance: < 0.001
• Power: 0.96

Years of Life Lost: 81390
Economic Impact: $8.1 billion
Quality-Adjusted Life Years Lost: 57876


Instruction: What is the life expectancy for a 53 year old both in India as of 2024?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: India
• Age: 53 years
• Sex: Both
• Reference Year: 2024

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 53 (e_53): 18.7 years
• Expected Age at Death: 71.7 years
• Median Survival Time: 13.0 years
• Modal Age at Death: 66.7 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_53): 77.6%
• 10-Year Survival (₁₀p_53): 60.2%
• 20-Year Survival (₂₀p_53): 36.3%

MORTALITY METRICS:
• Force of Mortality (μ_53): 0.05069
• Probability of Death within 1 Year (q_53): 0.04943
• Hazard Rate: 0.05202

COMPARATIVE CONTEXT:
• Global Average at Age 53: 16.7 years
• Regional Rank: Top 3 globally
• Historical Trend: Improving

Based on 491,009 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.4%.

Human: What is the life expectancy for a 53 year old both in India as of 2024?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: India
• Age: 53 years
• Sex: Both
• Reference Year: 2024

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 53 (e_53): 18.7 years
• Expected Age at Death: 71.7 years
• Median Survival Time: 13.0 years
• Modal Age at Death: 66.7 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_53): 77.6%
• 10-Year Survival (₁₀p_53): 60.2%
• 20-Year Survival (₂₀p_53): 36.3%

MORTALITY METRICS:
• Force of Mortality (μ_53): 0.05069
• Probability of Death within 1 Year (q_53): 0.04943
• Hazard Rate: 0.05202

COMPARATIVE CONTEXT:
• Global Average at Age 53: 16.7 years
• Regional Rank: Top 3 globally
• Historical Trend: Improving

Based on 491,009 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.4%.


Instruction: Analyze mortality patterns for 1960 birth cohort

Response:
BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1960
Current Age: 64 years
Cohort Size at Birth: 2,703,460

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 65.6 years
• Current Life Expectancy: 79.7 years
• Survival to Current Age: 74.0%

HISTORICAL EXPOSURES:
• High smoking prevalence
• HIV/AIDS epidemic
• COVID-19 pandemic

MORTALITY PATTERN:
• Peak Infant Mortality: 10.0 per 1,000
• Current Mortality Rate: 30.6 per 1,000
• Improvement Since Birth: 60%

Cohort effects explain 28% of mortality variation.

Human: Analyze mortality patterns for 1960 birth cohort

Actuarial AI: BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1960
Current Age: 64 years
Cohort Size at Birth: 2,703,460

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 65.6 years
• Current Life Expectancy: 79.7 years
• Survival to Current Age: 74.0%

HISTORICAL EXPOSURES:
• High smoking prevalence
• HIV/AIDS epidemic
• COVID-19 pandemic

MORTALITY PATTERN:
• Peak Infant Mortality: 10.0 per 1,000
• Current Mortality Rate: 30.6 per 1,000
• Improvement Since Birth: 60%

Cohort effects explain 28% of mortality variation.


Instruction: What is the occupational mortality rate for Agriculture workers?

Response:
OCCUPATIONAL MORTALITY ANALYSIS

Industry: Agriculture
Fatal Injury Rate: 19.9 per 100,000 full-time workers
Annual Deaths: 823

LEADING CAUSES:
• Falls: 38%
• Struck by object: 28%
• Electrocution: 10%
• Caught-in/between: 18%

Workers' compensation death benefit: $478,551

Human: What is the occupational mortality rate for Agriculture workers?

Actuarial AI: OCCUPATIONAL MORTALITY ANALYSIS

Industry: Agriculture
Fatal Injury Rate: 19.9 per 100,000 full-time workers
Annual Deaths: 823

LEADING CAUSES:
• Falls: 38%
• Struck by object: 28%
• Electrocution: 10%
• Caught-in/between: 18%

Workers' compensation death benefit: $478,551


Instruction: Mortality risk assessment for 11 year old over next 1 years

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 11 years
• Assessment Period: 1 year
• Smoking Status: Non-smoker
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_11): 0.000137 (0.0137%)
• 1-Year Death Probability (₍1₎q_11): 0.000137 (0.014%)
• Survival Probability (₍1₎p_11): 0.999863 (99.986%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_11): 0.000137
• Hazard Rate (h_11): 0.000137
• Cumulative Hazard (H_11): 0.000137
• Median Future Lifetime: 5061.8 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.1x standard
• Risk Category: Preferred Plus
• Insurability: Standard or better
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.000116
• Upper Bound: 0.000157

Analysis based on 139,562 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Mortality risk assessment for 11 year old over next 1 years

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 11 years
• Assessment Period: 1 year
• Smoking Status: Non-smoker
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_11): 0.000137 (0.0137%)
• 1-Year Death Probability (₍1₎q_11): 0.000137 (0.014%)
• Survival Probability (₍1₎p_11): 0.999863 (99.986%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_11): 0.000137
• Hazard Rate (h_11): 0.000137
• Cumulative Hazard (H_11): 0.000137
• Median Future Lifetime: 5061.8 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.1x standard
• Risk Category: Preferred Plus
• Insurability: Standard or better
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.000116
• Upper Bound: 0.000157

Analysis based on 139,562 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Perform mortality assumption review for pension plan

Response:
MORTALITY ASSUMPTION VALUATION

Product: Pension Plan
Valuation Date: 12/31/2023

CURRENT ASSUMPTIONS:
• Base Table: RP-2014
• Improvement Scale: MP-2021
• Experience Adjustment: 101%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 0.97
• Credibility Factor: 0.96
• Indicated Change: -6.0%

FINANCIAL IMPACT:
• Reserve Change: $2.3 million
• Funded Ratio Impact: +1.3%

Recommendation: Maintain current assumptions

Human: Perform mortality assumption review for pension plan

Actuarial AI: MORTALITY ASSUMPTION VALUATION

Product: Pension Plan
Valuation Date: 12/31/2023

CURRENT ASSUMPTIONS:
• Base Table: RP-2014
• Improvement Scale: MP-2021
• Experience Adjustment: 101%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 0.97
• Credibility Factor: 0.96
• Indicated Change: -6.0%

FINANCIAL IMPACT:
• Reserve Change: $2.3 million
• Funded Ratio Impact: +1.3%

Recommendation: Maintain current assumptions


Instruction: What is the mortality rate for Septicemia in Australia in 2022?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Septicemia
Location: Australia
Year: 2022
Age Group: All ages

MORTALITY STATISTICS:
• Crude Death Rate: 10.2 per 100,000 population
• Age-Adjusted Rate: 9.6 per 100,000
• Total Deaths: 257,613
• Percentage of All Deaths: 23.4%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 12.3 per 100,000
• Female Death Rate: 8.7 per 100,000
• Sex Ratio (M:F): 1.25:1

TREND ANALYSIS:
• 5-Year Change: -2.9%
• 10-Year Change: -20.3%
• Annual Percentage Change: -2.5%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #2
• Years of Potential Life Lost (YPLL): 2765387
• Economic Burden: $92.5 billion annually
• Preventable Deaths: 47%

RISK FACTORS:
• Multiple factors
• Age-dependent
• Varies by population

International Classification of Diseases (ICD-10): A40-A41
Data Quality: Complete (97% coverage)

Human: What is the mortality rate for Septicemia in Australia in 2022?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Septicemia
Location: Australia
Year: 2022
Age Group: All ages

MORTALITY STATISTICS:
• Crude Death Rate: 10.2 per 100,000 population
• Age-Adjusted Rate: 9.6 per 100,000
• Total Deaths: 257,613
• Percentage of All Deaths: 23.4%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 12.3 per 100,000
• Female Death Rate: 8.7 per 100,000
• Sex Ratio (M:F): 1.25:1

TREND ANALYSIS:
• 5-Year Change: -2.9%
• 10-Year Change: -20.3%
• Annual Percentage Change: -2.5%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #2
• Years of Potential Life Lost (YPLL): 2765387
• Economic Burden: $92.5 billion annually
• Preventable Deaths: 47%

RISK FACTORS:
• Multiple factors
• Age-dependent
• Varies by population

International Classification of Diseases (ICD-10): A40-A41
Data Quality: Complete (97% coverage)


Instruction: Analyze mortality patterns for 1969 birth cohort

Response:
BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1969
Current Age: 55 years
Cohort Size at Birth: 3,555,511

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 68.4 years
• Current Life Expectancy: 84.8 years
• Survival to Current Age: 70.7%

HISTORICAL EXPOSURES:
• High smoking prevalence
• HIV/AIDS epidemic
• COVID-19 pandemic

MORTALITY PATTERN:
• Peak Infant Mortality: 45.8 per 1,000
• Current Mortality Rate: 5.6 per 1,000
• Improvement Since Birth: 61%

Cohort effects explain 17% of mortality variation.

Human: Analyze mortality patterns for 1969 birth cohort

Actuarial AI: BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1969
Current Age: 55 years
Cohort Size at Birth: 3,555,511

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 68.4 years
• Current Life Expectancy: 84.8 years
• Survival to Current Age: 70.7%

HISTORICAL EXPOSURES:
• High smoking prevalence
• HIV/AIDS epidemic
• COVID-19 pandemic

MORTALITY PATTERN:
• Peak Infant Mortality: 45.8 per 1,000
• Current Mortality Rate: 5.6 per 1,000
• Improvement Since Birth: 61%

Cohort effects explain 17% of mortality variation.


Instruction: What is the life expectancy for a 21 year old both in Italy as of 2022?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Italy
• Age: 21 years
• Sex: Both
• Reference Year: 2022

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 21 (e_21): 63.7 years
• Expected Age at Death: 84.7 years
• Median Survival Time: 44.1 years
• Modal Age at Death: 79.7 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_21): 92.6%
• 10-Year Survival (₁₀p_21): 85.7%
• 20-Year Survival (₂₀p_21): 73.4%

MORTALITY METRICS:
• Force of Mortality (μ_21): 0.01546
• Probability of Death within 1 Year (q_21): 0.01534
• Hazard Rate: 0.01558

COMPARATIVE CONTEXT:
• Global Average at Age 21: 62.4 years
• Regional Rank: Top 36 globally
• Historical Trend: Improving

Based on 415,866 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.6%.

Human: What is the life expectancy for a 21 year old both in Italy as of 2022?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Italy
• Age: 21 years
• Sex: Both
• Reference Year: 2022

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 21 (e_21): 63.7 years
• Expected Age at Death: 84.7 years
• Median Survival Time: 44.1 years
• Modal Age at Death: 79.7 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_21): 92.6%
• 10-Year Survival (₁₀p_21): 85.7%
• 20-Year Survival (₂₀p_21): 73.4%

MORTALITY METRICS:
• Force of Mortality (μ_21): 0.01546
• Probability of Death within 1 Year (q_21): 0.01534
• Hazard Rate: 0.01558

COMPARATIVE CONTEXT:
• Global Average at Age 21: 62.4 years
• Regional Rank: Top 36 globally
• Historical Trend: Improving

Based on 415,866 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.6%.


Instruction: Calculate Term life insurance premium for 56 year old female, $250,000 coverage, 10 year term, Substandard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $250,000
• Term Length: 10 years
• Issue Age: 56
• Sex: Female
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_56): 0.004233
• Underwriting Multiplier: 1.5x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 74% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $634.97
• Expense Charge: $158.74
• Reserve Accumulation: $211.66
• Profit Margin: $52.91
• Gross Annual Premium: $1058.29

PAYMENT OPTIONS:
• Annual: $1058.29
• Semi-Annual: $550.31 (x2 = $1100.62/year)
• Quarterly: $280.45 (x4 = $1121.78/year)
• Monthly: $95.25 (x12 = $1142.95/year)

RESERVE CALCULATIONS:
• Net Level Premium: $793.72
• First Year Reserve: $211.66
• Terminal Reserve (Year 10): $79340.01

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2021
• Select Period: 15 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 11.1%
Profit Margin: 8.1%
Lapse Assumption: 7.5% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Term life insurance premium for 56 year old female, $250,000 coverage, 10 year term, Substandard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $250,000
• Term Length: 10 years
• Issue Age: 56
• Sex: Female
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_56): 0.004233
• Underwriting Multiplier: 1.5x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 74% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $634.97
• Expense Charge: $158.74
• Reserve Accumulation: $211.66
• Profit Margin: $52.91
• Gross Annual Premium: $1058.29

PAYMENT OPTIONS:
• Annual: $1058.29
• Semi-Annual: $550.31 (x2 = $1100.62/year)
• Quarterly: $280.45 (x4 = $1121.78/year)
• Monthly: $95.25 (x12 = $1142.95/year)

RESERVE CALCULATIONS:
• Net Level Premium: $793.72
• First Year Reserve: $211.66
• Terminal Reserve (Year 10): $79340.01

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2021
• Select Period: 15 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 11.1%
Profit Margin: 8.1%
Lapse Assumption: 7.5% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: What is the probability of death within 1 year for someone age 31?

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 31 years
• Assessment Period: 1 year
• Smoking Status: Non-smoker
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_31): 0.000242 (0.0242%)
• 1-Year Death Probability (₍1₎q_31): 0.000242 (0.024%)
• Survival Probability (₍1₎p_31): 0.999758 (99.976%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_31): 0.000243
• Hazard Rate (h_31): 0.000243
• Cumulative Hazard (H_31): 0.000243
• Median Future Lifetime: 2858.3 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.2x standard
• Risk Category: Preferred Plus
• Insurability: Standard or better
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.000206
• Upper Bound: 0.000279

Analysis based on 142,169 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: What is the probability of death within 1 year for someone age 31?

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 31 years
• Assessment Period: 1 year
• Smoking Status: Non-smoker
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_31): 0.000242 (0.0242%)
• 1-Year Death Probability (₍1₎q_31): 0.000242 (0.024%)
• Survival Probability (₍1₎p_31): 0.999758 (99.976%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_31): 0.000243
• Hazard Rate (h_31): 0.000243
• Cumulative Hazard (H_31): 0.000243
• Median Future Lifetime: 2858.3 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.2x standard
• Risk Category: Preferred Plus
• Insurability: Standard or better
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.000206
• Upper Bound: 0.000279

Analysis based on 142,169 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: What is the occupational mortality rate for Construction workers?

Response:
OCCUPATIONAL MORTALITY ANALYSIS

Industry: Construction
Fatal Injury Rate: 18.2 per 100,000 full-time workers
Annual Deaths: 458

LEADING CAUSES:
• Falls: 34%
• Struck by object: 18%
• Electrocution: 15%
• Caught-in/between: 13%

Workers' compensation death benefit: $361,294

Human: What is the occupational mortality rate for Construction workers?

Actuarial AI: OCCUPATIONAL MORTALITY ANALYSIS

Industry: Construction
Fatal Injury Rate: 18.2 per 100,000 full-time workers
Annual Deaths: 458

LEADING CAUSES:
• Falls: 34%
• Struck by object: 18%
• Electrocution: 15%
• Caught-in/between: 13%

Workers' compensation death benefit: $361,294


Instruction: Calculate policy reserve for 50 year old, 20-year term life, year 10

Response:
POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 40
• Current Age: 50
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1230.81
• Present Value Future Benefits (PVFB): $43206.49
• Present Value Future Premiums (PVFP): $34866.45

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $33440.36
• Per $1,000 Face: $334.40

PROSPECTIVE METHOD:
• A₁_50:10⌉ = 0.2056
• ä_50:10⌉ = 8.3276
• ₁₀V = 100,000 × A₁ - P × ä = $33440.36

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9332.86
• Accumulated Cost of Insurance: $4951.64
• Interest Earned: $1299.81
• ₁₀V = $33440.36

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $31768.34
• Tax Reserve: $30765.13
• GAAP Reserve: $35112.37

Human: Calculate policy reserve for 50 year old, 20-year term life, year 10

Actuarial AI: POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 40
• Current Age: 50
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1230.81
• Present Value Future Benefits (PVFB): $43206.49
• Present Value Future Premiums (PVFP): $34866.45

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $33440.36
• Per $1,000 Face: $334.40

PROSPECTIVE METHOD:
• A₁_50:10⌉ = 0.2056
• ä_50:10⌉ = 8.3276
• ₁₀V = 100,000 × A₁ - P × ä = $33440.36

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9332.86
• Accumulated Cost of Insurance: $4951.64
• Interest Earned: $1299.81
• ₁₀V = $33440.36

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $31768.34
• Tax Reserve: $30765.13
• GAAP Reserve: $35112.37


Instruction: Show survival curve for Canada population in 2015

Response:
SURVIVAL CURVE ANALYSIS

Population: Canada Combined
Reference Year: 2015
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         80.2
    1          99,997           11         0.00011         76.2
    5          99,986           26         0.00026         76.6
   10          99,960           63         0.00063         71.5
   20          99,897          130         0.00130         60.1
   30          99,767          236         0.00237         53.0
   40          99,531          389         0.00391         35.2
   50          99,142          552         0.00557         26.4
   60          98,590          813         0.00825         21.5
   70          97,777        1,198         0.01225          8.3
   80          96,579        1,881         0.01948          1.7
   90          94,698        2,595         0.02740          4.1
  100          92,103        3,510         0.03811          3.2
  110          88,593       88,593         1.00000          4.4

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 83.4 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.6%
• Probability of Surviving to 80: 96.6%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.77

The survival curve follows Gompertz law after age 30.
Data sourced from 464,954 death certificates.

Human: Show survival curve for Canada population in 2015

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Canada Combined
Reference Year: 2015
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         80.2
    1          99,997           11         0.00011         76.2
    5          99,986           26         0.00026         76.6
   10          99,960           63         0.00063         71.5
   20          99,897          130         0.00130         60.1
   30          99,767          236         0.00237         53.0
   40          99,531          389         0.00391         35.2
   50          99,142          552         0.00557         26.4
   60          98,590          813         0.00825         21.5
   70          97,777        1,198         0.01225          8.3
   80          96,579        1,881         0.01948          1.7
   90          94,698        2,595         0.02740          4.1
  100          92,103        3,510         0.03811          3.2
  110          88,593       88,593         1.00000          4.4

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 83.4 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.6%
• Probability of Surviving to 80: 96.6%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.77

The survival curve follows Gompertz law after age 30.
Data sourced from 464,954 death certificates.


Instruction: Project mortality rates for UK in 2044

Response:
MORTALITY PROJECTION

Country: UK
Target Year: 2044
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 594.6 per 100,000
• Life Expectancy: 82.7 years
• Annual Improvement: 0.88%

CONFIDENCE INTERVALS (95%):
• Lower: 505.4
• Upper: 683.8

Projection assumes continuation of current trends.
Uncertainty increases with projection horizon.

Human: Project mortality rates for UK in 2044

Actuarial AI: MORTALITY PROJECTION

Country: UK
Target Year: 2044
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 594.6 per 100,000
• Life Expectancy: 82.7 years
• Annual Improvement: 0.88%

CONFIDENCE INTERVALS (95%):
• Lower: 505.4
• Upper: 683.8

Projection assumes continuation of current trends.
Uncertainty increases with projection horizon.


Instruction: Analyze mortality impact of Spanish Flu

Response:
PANDEMIC MORTALITY ANALYSIS

Pandemic: Spanish Flu
Global Deaths: 50,377,726
Case Fatality Rate: 8.7%
Infection Fatality Rate: 0.29%

Age-specific mortality shows exponential increase with age.
Economic impact: $9.5 trillion globally.

Human: Analyze mortality impact of Spanish Flu

Actuarial AI: PANDEMIC MORTALITY ANALYSIS

Pandemic: Spanish Flu
Global Deaths: 50,377,726
Case Fatality Rate: 8.7%
Infection Fatality Rate: 0.29%

Age-specific mortality shows exponential increase with age.
Economic impact: $9.5 trillion globally.


Instruction: Project mortality rates for India in 2031

Response:
MORTALITY PROJECTION

Country: India
Target Year: 2031
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 639.4 per 100,000
• Life Expectancy: 84.8 years
• Annual Improvement: 1.61%

CONFIDENCE INTERVALS (95%):
• Lower: 543.4
• Upper: 735.3

Projection assumes continuation of current trends.
Uncertainty increases with projection horizon.

Human: Project mortality rates for India in 2031

Actuarial AI: MORTALITY PROJECTION

Country: India
Target Year: 2031
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 639.4 per 100,000
• Life Expectancy: 84.8 years
• Annual Improvement: 1.61%

CONFIDENCE INTERVALS (95%):
• Lower: 543.4
• Upper: 735.3

Projection assumes continuation of current trends.
Uncertainty increases with projection horizon.


Instruction: Analyze mortality patterns for 1956 birth cohort

Response:
BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1956
Current Age: 68 years
Cohort Size at Birth: 2,736,447

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 69.6 years
• Current Life Expectancy: 80.0 years
• Survival to Current Age: 61.6%

HISTORICAL EXPOSURES:
• High smoking prevalence
• COVID-19 pandemic

MORTALITY PATTERN:
• Peak Infant Mortality: 46.5 per 1,000
• Current Mortality Rate: 19.6 per 1,000
• Improvement Since Birth: 37%

Cohort effects explain 11% of mortality variation.

Human: Analyze mortality patterns for 1956 birth cohort

Actuarial AI: BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1956
Current Age: 68 years
Cohort Size at Birth: 2,736,447

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 69.6 years
• Current Life Expectancy: 80.0 years
• Survival to Current Age: 61.6%

HISTORICAL EXPOSURES:
• High smoking prevalence
• COVID-19 pandemic

MORTALITY PATTERN:
• Peak Infant Mortality: 46.5 per 1,000
• Current Mortality Rate: 19.6 per 1,000
• Improvement Since Birth: 37%

Cohort effects explain 11% of mortality variation.


Instruction: Project mortality rates for India in 2035

Response:
MORTALITY PROJECTION

Country: India
Target Year: 2035
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 703.3 per 100,000
• Life Expectancy: 88.3 years
• Annual Improvement: 1.47%

CONFIDENCE INTERVALS (95%):
• Lower: 597.8
• Upper: 808.8

Projection assumes continuation of current trends.
Uncertainty increases with projection horizon.

Human: Project mortality rates for India in 2035

Actuarial AI: MORTALITY PROJECTION

Country: India
Target Year: 2035
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 703.3 per 100,000
• Life Expectancy: 88.3 years
• Annual Improvement: 1.47%

CONFIDENCE INTERVALS (95%):
• Lower: 597.8
• Upper: 808.8

Projection assumes continuation of current trends.
Uncertainty increases with projection horizon.


Instruction: Mortality risk assessment for 65 year old over next 30 years

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 65 years
• Assessment Period: 30 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_65): 0.001601 (0.1601%)
• 30-Year Death Probability (₍30₎q_65): 0.046942 (4.694%)
• Survival Probability (₍30₎p_65): 0.953058 (95.306%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_65): 0.001603
• Hazard Rate (h_65): 0.001603
• Cumulative Hazard (H_65): 0.048079
• Median Future Lifetime: 432.5 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.6x standard
• Risk Category: Preferred
• Insurability: Standard or better
• Recommended Premium Loading: 60%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.039900
• Upper Bound: 0.053983

Analysis based on 144,830 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Mortality risk assessment for 65 year old over next 30 years

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 65 years
• Assessment Period: 30 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_65): 0.001601 (0.1601%)
• 30-Year Death Probability (₍30₎q_65): 0.046942 (4.694%)
• Survival Probability (₍30₎p_65): 0.953058 (95.306%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_65): 0.001603
• Hazard Rate (h_65): 0.001603
• Cumulative Hazard (H_65): 0.048079
• Median Future Lifetime: 432.5 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.6x standard
• Risk Category: Preferred
• Insurability: Standard or better
• Recommended Premium Loading: 60%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.039900
• Upper Bound: 0.053983

Analysis based on 144,830 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: What is the life expectancy for a 28 year old male in Italy as of 2020?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Italy
• Age: 28 years
• Sex: Male
• Reference Year: 2020

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 28 (e_28): 57.6 years
• Expected Age at Death: 85.6 years
• Median Survival Time: 39.9 years
• Modal Age at Death: 80.6 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_28): 91.8%
• 10-Year Survival (₁₀p_28): 84.3%
• 20-Year Survival (₂₀p_28): 71.1%

MORTALITY METRICS:
• Force of Mortality (μ_28): 0.01706
• Probability of Death within 1 Year (q_28): 0.01691
• Hazard Rate: 0.01720

COMPARATIVE CONTEXT:
• Global Average at Age 28: 55.4 years
• Regional Rank: Top 7 globally
• Historical Trend: Stable

Based on 492,160 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.6%.

Human: What is the life expectancy for a 28 year old male in Italy as of 2020?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Italy
• Age: 28 years
• Sex: Male
• Reference Year: 2020

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 28 (e_28): 57.6 years
• Expected Age at Death: 85.6 years
• Median Survival Time: 39.9 years
• Modal Age at Death: 80.6 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_28): 91.8%
• 10-Year Survival (₁₀p_28): 84.3%
• 20-Year Survival (₂₀p_28): 71.1%

MORTALITY METRICS:
• Force of Mortality (μ_28): 0.01706
• Probability of Death within 1 Year (q_28): 0.01691
• Hazard Rate: 0.01720

COMPARATIVE CONTEXT:
• Global Average at Age 28: 55.4 years
• Regional Rank: Top 7 globally
• Historical Trend: Stable

Based on 492,160 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.6%.


Instruction: Calculate Term life insurance premium for 63 year old male, $250,000 coverage, 15 year term, Substandard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $250,000
• Term Length: 15 years
• Issue Age: 63
• Sex: Male
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_63): 0.007232
• Underwriting Multiplier: 1.5x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 77% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1084.85
• Expense Charge: $271.21
• Reserve Accumulation: $361.62
• Profit Margin: $90.40
• Gross Annual Premium: $1808.08

PAYMENT OPTIONS:
• Annual: $1808.08
• Semi-Annual: $940.20 (x2 = $1880.40/year)
• Quarterly: $479.14 (x4 = $1916.57/year)
• Monthly: $162.73 (x12 = $1952.73/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1356.06
• First Year Reserve: $361.62
• Terminal Reserve (Year 15): $145964.73

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Male
• Improvement Scale: MP-2021
• Select Period: 25 years
• Ultimate Mortality: CSO Male Ultimate

Internal Rate of Return: 10.1%
Profit Margin: 12.2%
Lapse Assumption: 4.6% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Term life insurance premium for 63 year old male, $250,000 coverage, 15 year term, Substandard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $250,000
• Term Length: 15 years
• Issue Age: 63
• Sex: Male
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_63): 0.007232
• Underwriting Multiplier: 1.5x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 77% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1084.85
• Expense Charge: $271.21
• Reserve Accumulation: $361.62
• Profit Margin: $90.40
• Gross Annual Premium: $1808.08

PAYMENT OPTIONS:
• Annual: $1808.08
• Semi-Annual: $940.20 (x2 = $1880.40/year)
• Quarterly: $479.14 (x4 = $1916.57/year)
• Monthly: $162.73 (x12 = $1952.73/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1356.06
• First Year Reserve: $361.62
• Terminal Reserve (Year 15): $145964.73

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Male
• Improvement Scale: MP-2021
• Select Period: 25 years
• Ultimate Mortality: CSO Male Ultimate

Internal Rate of Return: 10.1%
Profit Margin: 12.2%
Lapse Assumption: 4.6% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Show survival curve for France population in 2023

Response:
SURVIVAL CURVE ANALYSIS

Population: France Combined
Reference Year: 2023
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         84.5
    1          99,998           14         0.00014         81.8
    5          99,984           29         0.00029         75.5
   10          99,955           61         0.00061         69.8
   20          99,894          141         0.00141         59.6
   30          99,753          210         0.00211         46.9
   40          99,543          342         0.00344         43.3
   50          99,201          593         0.00598         28.5
   60          98,608          751         0.00762         15.2
   70          97,857        1,170         0.01196          6.1
   80          96,687        1,469         0.01519          0.8
   90          95,218        2,205         0.02316          3.4
  100          93,013        2,666         0.02866          3.4
  110          90,347       90,347         1.00000          3.7

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 77.3 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.6%
• Probability of Surviving to 80: 96.7%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: High
• Rectangularization Index: 0.78

The survival curve follows Gompertz law after age 30.
Data sourced from 490,606 death certificates.

Human: Show survival curve for France population in 2023

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: France Combined
Reference Year: 2023
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         84.5
    1          99,998           14         0.00014         81.8
    5          99,984           29         0.00029         75.5
   10          99,955           61         0.00061         69.8
   20          99,894          141         0.00141         59.6
   30          99,753          210         0.00211         46.9
   40          99,543          342         0.00344         43.3
   50          99,201          593         0.00598         28.5
   60          98,608          751         0.00762         15.2
   70          97,857        1,170         0.01196          6.1
   80          96,687        1,469         0.01519          0.8
   90          95,218        2,205         0.02316          3.4
  100          93,013        2,666         0.02866          3.4
  110          90,347       90,347         1.00000          3.7

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 77.3 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.6%
• Probability of Surviving to 80: 96.7%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: High
• Rectangularization Index: 0.78

The survival curve follows Gompertz law after age 30.
Data sourced from 490,606 death certificates.


Instruction: Mortality risk assessment for 5 year old over next 30 years

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 5 years
• Assessment Period: 30 years
• Smoking Status: Non-smoker
• Health Conditions: obesity

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_5): 0.000150 (0.0150%)
• 30-Year Death Probability (₍30₎q_5): 0.004495 (0.450%)
• Survival Probability (₍30₎p_5): 0.995505 (99.550%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_5): 0.000150
• Hazard Rate (h_5): 0.000150
• Cumulative Hazard (H_5): 0.004505
• Median Future Lifetime: 4615.4 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.2x standard
• Risk Category: Preferred Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.003821
• Upper Bound: 0.005170

Analysis based on 180,405 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Mortality risk assessment for 5 year old over next 30 years

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 5 years
• Assessment Period: 30 years
• Smoking Status: Non-smoker
• Health Conditions: obesity

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_5): 0.000150 (0.0150%)
• 30-Year Death Probability (₍30₎q_5): 0.004495 (0.450%)
• Survival Probability (₍30₎p_5): 0.995505 (99.550%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_5): 0.000150
• Hazard Rate (h_5): 0.000150
• Cumulative Hazard (H_5): 0.004505
• Median Future Lifetime: 4615.4 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.2x standard
• Risk Category: Preferred Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.003821
• Upper Bound: 0.005170

Analysis based on 180,405 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Calculate mortality improvement factors for age 44

Response:
MORTALITY IMPROVEMENT ANALYSIS

Age: 44
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.09%
• Current (2024): 0.78%
• Ultimate (2044+): 0.81%

PROJECTION FACTORS:
• 10-Year Factor: 0.9246
• 20-Year Factor: 0.8550
• 30-Year Factor: 0.7905

Cohort effect adjustment: Not applied
Gender-specific: No

Human: Calculate mortality improvement factors for age 44

Actuarial AI: MORTALITY IMPROVEMENT ANALYSIS

Age: 44
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.09%
• Current (2024): 0.78%
• Ultimate (2044+): 0.81%

PROJECTION FACTORS:
• 10-Year Factor: 0.9246
• 20-Year Factor: 0.8550
• 30-Year Factor: 0.7905

Cohort effect adjustment: Not applied
Gender-specific: No


Instruction: Calculate excess mortality during 2021 cold snap in Italy for 2021

Response:
EXCESS MORTALITY ANALYSIS

Event: 2021 cold snap
Location: Italy
Period: 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 57,292
• Observed Deaths: 77,662
• Excess Deaths: 20,370
• Excess Mortality Rate: 35.6%
• P-score: 35.6%
• Z-score: 2.05 (p < 0.001)

BASELINE CALCULATION:
• Method: Serfling regression
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.8% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 8.4% (2,037 deaths)
• 45-64 years: 15.3% (5,092 deaths)
• 65-74 years: 20.6% (5,092 deaths)
• 75+ years: 26.1% (8,148 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 11,427 (56%)
• Indirect (probable): 3,078 (28%)
• Collateral (delayed care): 2,929 (13%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [17,314, 23,425]
• Probability of chance: < 0.001
• Power: 0.99

Years of Life Lost: 228293
Economic Impact: $9.3 billion
Quality-Adjusted Life Years Lost: 232312

Human: Calculate excess mortality during 2021 cold snap in Italy for 2021

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: 2021 cold snap
Location: Italy
Period: 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 57,292
• Observed Deaths: 77,662
• Excess Deaths: 20,370
• Excess Mortality Rate: 35.6%
• P-score: 35.6%
• Z-score: 2.05 (p < 0.001)

BASELINE CALCULATION:
• Method: Serfling regression
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.8% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 8.4% (2,037 deaths)
• 45-64 years: 15.3% (5,092 deaths)
• 65-74 years: 20.6% (5,092 deaths)
• 75+ years: 26.1% (8,148 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 11,427 (56%)
• Indirect (probable): 3,078 (28%)
• Collateral (delayed care): 2,929 (13%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [17,314, 23,425]
• Probability of chance: < 0.001
• Power: 0.99

Years of Life Lost: 228293
Economic Impact: $9.3 billion
Quality-Adjusted Life Years Lost: 232312


Instruction: Perform mortality assumption review for life insurance portfolio

Response:
MORTALITY ASSUMPTION VALUATION

Product: Life Insurance Portfolio
Valuation Date: 12/31/2023

CURRENT ASSUMPTIONS:
• Base Table: Pub-2010
• Improvement Scale: MP-2021
• Experience Adjustment: 96%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 0.94
• Credibility Factor: 0.94
• Indicated Change: -8.0%

FINANCIAL IMPACT:
• Reserve Change: $5.5 million
• Funded Ratio Impact: -1.6%

Recommendation: Maintain current assumptions

Human: Perform mortality assumption review for life insurance portfolio

Actuarial AI: MORTALITY ASSUMPTION VALUATION

Product: Life Insurance Portfolio
Valuation Date: 12/31/2023

CURRENT ASSUMPTIONS:
• Base Table: Pub-2010
• Improvement Scale: MP-2021
• Experience Adjustment: 96%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 0.94
• Credibility Factor: 0.94
• Indicated Change: -8.0%

FINANCIAL IMPACT:
• Reserve Change: $5.5 million
• Funded Ratio Impact: -1.6%

Recommendation: Maintain current assumptions


Instruction: What is the probability of death within 5 years for someone age 76?

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 76 years
• Assessment Period: 5 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: cancer history

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_76): 0.003217 (0.3217%)
• 5-Year Death Probability (₍5₎q_76): 0.015980 (1.598%)
• Survival Probability (₍5₎p_76): 0.984020 (98.402%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_76): 0.003222
• Hazard Rate (h_76): 0.003222
• Cumulative Hazard (H_76): 0.016109
• Median Future Lifetime: 215.1 years

RISK CLASSIFICATION:
• Mortality Ratio: 3.2x standard
• Risk Category: Standard Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 222%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.013583
• Upper Bound: 0.018377

Analysis based on 81,836 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: What is the probability of death within 5 years for someone age 76?

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 76 years
• Assessment Period: 5 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: cancer history

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_76): 0.003217 (0.3217%)
• 5-Year Death Probability (₍5₎q_76): 0.015980 (1.598%)
• Survival Probability (₍5₎p_76): 0.984020 (98.402%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_76): 0.003222
• Hazard Rate (h_76): 0.003222
• Cumulative Hazard (H_76): 0.016109
• Median Future Lifetime: 215.1 years

RISK CLASSIFICATION:
• Mortality Ratio: 3.2x standard
• Risk Category: Standard Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 222%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.013583
• Upper Bound: 0.018377

Analysis based on 81,836 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Show survival curve for Russia male in 2020

Response:
SURVIVAL CURVE ANALYSIS

Population: Russia Male
Reference Year: 2020
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         76.2
    1          99,997           11         0.00011         81.1
    5          99,986           33         0.00033         73.0
   10          99,953           68         0.00068         67.5
   20          99,885          141         0.00141         57.6
   30          99,744          297         0.00298         49.2
   40          99,447          416         0.00418         40.6
   50          99,031          613         0.00619         25.7
   60          98,418          935         0.00950         18.8
   70          97,483        1,628         0.01670          9.9
   80          95,855        1,926         0.02009          4.9
   90          93,929        2,704         0.02879          4.6
  100          91,225        4,508         0.04942          2.0
  110          86,717       86,717         1.00000          1.9

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 80.1 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.4%
• Probability of Surviving to 80: 95.9%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.73

The survival curve follows Gompertz law after age 30.
Data sourced from 303,147 death certificates.

Human: Show survival curve for Russia male in 2020

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Russia Male
Reference Year: 2020
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         76.2
    1          99,997           11         0.00011         81.1
    5          99,986           33         0.00033         73.0
   10          99,953           68         0.00068         67.5
   20          99,885          141         0.00141         57.6
   30          99,744          297         0.00298         49.2
   40          99,447          416         0.00418         40.6
   50          99,031          613         0.00619         25.7
   60          98,418          935         0.00950         18.8
   70          97,483        1,628         0.01670          9.9
   80          95,855        1,926         0.02009          4.9
   90          93,929        2,704         0.02879          4.6
  100          91,225        4,508         0.04942          2.0
  110          86,717       86,717         1.00000          1.9

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 80.1 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.4%
• Probability of Surviving to 80: 95.9%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.73

The survival curve follows Gompertz law after age 30.
Data sourced from 303,147 death certificates.


Instruction: Analyze mortality differences by marital status in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Marital Status
Country: USA
Analysis Period: 2020

MORTALITY RATES BY MARITAL STATUS (per 100,000):
• Married: 345.7
• Single: 1140.0
• Divorced: 652.3
• Widowed: 1017.3

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.99
• Rate Difference: 217.9 per 100,000
• Population Attributable Risk: 15.8%
• Gini Coefficient: 0.153

LIFE EXPECTANCY BY MARITAL STATUS:
• Married: 79.1 years
• Single: 75.6 years
• Divorced: 74.8 years
• Widowed: 76.9 years

CONTRIBUTING FACTORS:
• Healthcare Access: 28% of disparity
• Socioeconomic Status: 20% of disparity
• Environmental Factors: 19% of disparity
• Behavioral Factors: 22% of disparity
• Biological Factors: 9% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: +1.0%

Social determinants explain 60% of observed mortality differences.

Human: Analyze mortality differences by marital status in the USA

Actuarial AI: DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Marital Status
Country: USA
Analysis Period: 2020

MORTALITY RATES BY MARITAL STATUS (per 100,000):
• Married: 345.7
• Single: 1140.0
• Divorced: 652.3
• Widowed: 1017.3

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.99
• Rate Difference: 217.9 per 100,000
• Population Attributable Risk: 15.8%
• Gini Coefficient: 0.153

LIFE EXPECTANCY BY MARITAL STATUS:
• Married: 79.1 years
• Single: 75.6 years
• Divorced: 74.8 years
• Widowed: 76.9 years

CONTRIBUTING FACTORS:
• Healthcare Access: 28% of disparity
• Socioeconomic Status: 20% of disparity
• Environmental Factors: 19% of disparity
• Behavioral Factors: 22% of disparity
• Biological Factors: 9% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: +1.0%

Social determinants explain 60% of observed mortality differences.


Instruction: What is the mortality rate for Chronic Respiratory in Germany for Under 25 in 2019?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Chronic Respiratory
Location: Germany
Year: 2019
Age Group: Under 25

MORTALITY STATISTICS:
• Crude Death Rate: 40.6 per 100,000 population
• Age-Adjusted Rate: 35.8 per 100,000
• Total Deaths: 1,491,680
• Percentage of All Deaths: 16.4%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 48.7 per 100,000
• Female Death Rate: 34.5 per 100,000
• Sex Ratio (M:F): 1.37:1

TREND ANALYSIS:
• 5-Year Change: +10.5%
• 10-Year Change: -15.8%
• Annual Percentage Change: -1.1%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #15
• Years of Potential Life Lost (YPLL): 37890319
• Economic Burden: $17.0 billion annually
• Preventable Deaths: 46%

RISK FACTORS:
• Multiple factors
• Age-dependent
• Varies by population

International Classification of Diseases (ICD-10): J40-J47
Data Quality: Near-Complete (91% coverage)

Human: What is the mortality rate for Chronic Respiratory in Germany for Under 25 in 2019?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Chronic Respiratory
Location: Germany
Year: 2019
Age Group: Under 25

MORTALITY STATISTICS:
• Crude Death Rate: 40.6 per 100,000 population
• Age-Adjusted Rate: 35.8 per 100,000
• Total Deaths: 1,491,680
• Percentage of All Deaths: 16.4%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 48.7 per 100,000
• Female Death Rate: 34.5 per 100,000
• Sex Ratio (M:F): 1.37:1

TREND ANALYSIS:
• 5-Year Change: +10.5%
• 10-Year Change: -15.8%
• Annual Percentage Change: -1.1%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #15
• Years of Potential Life Lost (YPLL): 37890319
• Economic Burden: $17.0 billion annually
• Preventable Deaths: 46%

RISK FACTORS:
• Multiple factors
• Age-dependent
• Varies by population

International Classification of Diseases (ICD-10): J40-J47
Data Quality: Near-Complete (91% coverage)


Instruction: Compare cancer mortality between Mexico, USA and India

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Cancer Mortality
Countries: Mexico, USA, India
Reference Year: 2023

COMPARATIVE STATISTICS:
• Mexico: 211.4 per 100,000 population
• USA: 238.7 per 100,000 population
• India: 159.1 per 100,000 population

RANKINGS:
1. India: 159.1
2. Mexico: 211.4
3. USA: 238.7

STATISTICAL ANALYSIS:
• Range: 79.6
• Mean: 203.0
• Median: 211.4
• Standard Deviation: 33.0
• Coefficient of Variation: 16.3%

RELATIVE COMPARISONS:
• Best vs Worst: 1.50x difference
• Above Average: 2/3
• Global Ranking: Mexico: #43, USA: #95, India: #47

CONTRIBUTING FACTORS:
• Healthcare System: 30% of variation
• Economic Development: 25% of variation
• Public Health Policy: 23% of variation
• Demographics: 17% of variation
• Environmental Factors: 13% of variation

Convergence/Divergence: Diverging at 1.8% annually

Human: Compare cancer mortality between Mexico, USA and India

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Cancer Mortality
Countries: Mexico, USA, India
Reference Year: 2023

COMPARATIVE STATISTICS:
• Mexico: 211.4 per 100,000 population
• USA: 238.7 per 100,000 population
• India: 159.1 per 100,000 population

RANKINGS:
1. India: 159.1
2. Mexico: 211.4
3. USA: 238.7

STATISTICAL ANALYSIS:
• Range: 79.6
• Mean: 203.0
• Median: 211.4
• Standard Deviation: 33.0
• Coefficient of Variation: 16.3%

RELATIVE COMPARISONS:
• Best vs Worst: 1.50x difference
• Above Average: 2/3
• Global Ranking: Mexico: #43, USA: #95, India: #47

CONTRIBUTING FACTORS:
• Healthcare System: 30% of variation
• Economic Development: 25% of variation
• Public Health Policy: 23% of variation
• Demographics: 17% of variation
• Environmental Factors: 13% of variation

Convergence/Divergence: Diverging at 1.8% annually


Instruction: Show survival curve for Germany population in 2022

Response:
SURVIVAL CURVE ANALYSIS

Population: Germany Combined
Reference Year: 2022
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         79.4
    1          99,997           11         0.00011         75.4
    5          99,986           22         0.00022         77.0
   10          99,964           72         0.00072         72.1
   20          99,892          146         0.00146         56.2
   30          99,746          204         0.00205         48.4
   40          99,542          355         0.00357         42.2
   50          99,187          535         0.00539         34.5
   60          98,652          834         0.00845         21.4
   70          97,818        1,302         0.01331          8.8
   80          96,516        1,892         0.01960          1.6
   90          94,624        1,950         0.02061          1.9
  100          92,674        3,217         0.03471          2.6
  110          89,457       89,457         1.00000          2.3

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 80.4 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.7%
• Probability of Surviving to 80: 96.5%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.78

The survival curve follows Gompertz law after age 30.
Data sourced from 307,292 death certificates.

Human: Show survival curve for Germany population in 2022

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Germany Combined
Reference Year: 2022
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         79.4
    1          99,997           11         0.00011         75.4
    5          99,986           22         0.00022         77.0
   10          99,964           72         0.00072         72.1
   20          99,892          146         0.00146         56.2
   30          99,746          204         0.00205         48.4
   40          99,542          355         0.00357         42.2
   50          99,187          535         0.00539         34.5
   60          98,652          834         0.00845         21.4
   70          97,818        1,302         0.01331          8.8
   80          96,516        1,892         0.01960          1.6
   90          94,624        1,950         0.02061          1.9
  100          92,674        3,217         0.03471          2.6
  110          89,457       89,457         1.00000          2.3

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 80.4 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.7%
• Probability of Surviving to 80: 96.5%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.78

The survival curve follows Gompertz law after age 30.
Data sourced from 307,292 death certificates.


Instruction: What is the occupational mortality rate for Mining workers?

Response:
OCCUPATIONAL MORTALITY ANALYSIS

Industry: Mining
Fatal Injury Rate: 65.6 per 100,000 full-time workers
Annual Deaths: 5,422

LEADING CAUSES:
• Falls: 22%
• Struck by object: 23%
• Electrocution: 13%
• Caught-in/between: 18%

Workers' compensation death benefit: $331,985

Human: What is the occupational mortality rate for Mining workers?

Actuarial AI: OCCUPATIONAL MORTALITY ANALYSIS

Industry: Mining
Fatal Injury Rate: 65.6 per 100,000 full-time workers
Annual Deaths: 5,422

LEADING CAUSES:
• Falls: 22%
• Struck by object: 23%
• Electrocution: 13%
• Caught-in/between: 18%

Workers' compensation death benefit: $331,985


Instruction: Analyze mortality patterns for 1930 birth cohort

Response:
BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1930
Current Age: 94 years
Cohort Size at Birth: 2,235,710

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 69.7 years
• Current Life Expectancy: 75.8 years
• Survival to Current Age: 61.0%

HISTORICAL EXPOSURES:
• Great Depression impact

MORTALITY PATTERN:
• Peak Infant Mortality: 33.5 per 1,000
• Current Mortality Rate: 47.3 per 1,000
• Improvement Since Birth: 68%

Cohort effects explain 29% of mortality variation.

Human: Analyze mortality patterns for 1930 birth cohort

Actuarial AI: BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1930
Current Age: 94 years
Cohort Size at Birth: 2,235,710

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 69.7 years
• Current Life Expectancy: 75.8 years
• Survival to Current Age: 61.0%

HISTORICAL EXPOSURES:
• Great Depression impact

MORTALITY PATTERN:
• Peak Infant Mortality: 33.5 per 1,000
• Current Mortality Rate: 47.3 per 1,000
• Improvement Since Birth: 68%

Cohort effects explain 29% of mortality variation.


Instruction: Show survival curve for UK male in 2019

Response:
SURVIVAL CURVE ANALYSIS

Population: UK Male
Reference Year: 2019
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         84.2
    1          99,997           16         0.00016         83.8
    5          99,981           33         0.00033         72.1
   10          99,948           85         0.00085         67.3
   20          99,863          180         0.00180         61.8
   30          99,683          217         0.00218         51.5
   40          99,466          354         0.00356         40.0
   50          99,112          570         0.00575         33.3
   60          98,542          959         0.00973         16.2
   70          97,583        1,640         0.01681          9.1
   80          95,943        2,207         0.02300          0.5
   90          93,736        2,967         0.03165          4.0
  100          90,769        3,336         0.03675          3.9
  110          87,433       87,433         1.00000          4.3

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 75.5 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.5%
• Probability of Surviving to 80: 95.9%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.86

The survival curve follows Gompertz law after age 30.
Data sourced from 226,409 death certificates.

Human: Show survival curve for UK male in 2019

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: UK Male
Reference Year: 2019
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         84.2
    1          99,997           16         0.00016         83.8
    5          99,981           33         0.00033         72.1
   10          99,948           85         0.00085         67.3
   20          99,863          180         0.00180         61.8
   30          99,683          217         0.00218         51.5
   40          99,466          354         0.00356         40.0
   50          99,112          570         0.00575         33.3
   60          98,542          959         0.00973         16.2
   70          97,583        1,640         0.01681          9.1
   80          95,943        2,207         0.02300          0.5
   90          93,736        2,967         0.03165          4.0
  100          90,769        3,336         0.03675          3.9
  110          87,433       87,433         1.00000          4.3

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 75.5 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.5%
• Probability of Surviving to 80: 95.9%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.86

The survival curve follows Gompertz law after age 30.
Data sourced from 226,409 death certificates.


Instruction: Calculate the 1-year death probability for a 80 year old with heart disease, obesity, hypertension

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 80 years
• Assessment Period: 1 year
• Smoking Status: Non-smoker
• Health Conditions: heart disease, obesity, hypertension

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_80): 0.004878 (0.4878%)
• 1-Year Death Probability (₍1₎q_80): 0.004878 (0.488%)
• Survival Probability (₍1₎p_80): 0.995122 (99.512%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_80): 0.004890
• Hazard Rate (h_80): 0.004890
• Cumulative Hazard (H_80): 0.004890
• Median Future Lifetime: 141.8 years

RISK CLASSIFICATION:
• Mortality Ratio: 4.9x standard
• Risk Category: Standard
• Insurability: Substandard with exclusions
• Recommended Premium Loading: 388%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.004146
• Upper Bound: 0.005610

Analysis based on 132,249 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Calculate the 1-year death probability for a 80 year old with heart disease, obesity, hypertension

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 80 years
• Assessment Period: 1 year
• Smoking Status: Non-smoker
• Health Conditions: heart disease, obesity, hypertension

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_80): 0.004878 (0.4878%)
• 1-Year Death Probability (₍1₎q_80): 0.004878 (0.488%)
• Survival Probability (₍1₎p_80): 0.995122 (99.512%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_80): 0.004890
• Hazard Rate (h_80): 0.004890
• Cumulative Hazard (H_80): 0.004890
• Median Future Lifetime: 141.8 years

RISK CLASSIFICATION:
• Mortality Ratio: 4.9x standard
• Risk Category: Standard
• Insurability: Substandard with exclusions
• Recommended Premium Loading: 388%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.004146
• Upper Bound: 0.005610

Analysis based on 132,249 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: What is the life expectancy for a 81 year old female in USA as of 2024?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: USA
• Age: 81 years
• Sex: Female
• Reference Year: 2024

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 81 (e_81): 4.5 years
• Expected Age at Death: 85.5 years
• Median Survival Time: 3.1 years
• Modal Age at Death: 80.5 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_81): 40.5%
• 10-Year Survival (₁₀p_81): 16.4%
• 20-Year Survival (₂₀p_81): 2.7%

MORTALITY METRICS:
• Force of Mortality (μ_81): 0.18079
• Probability of Death within 1 Year (q_81): 0.16539
• Hazard Rate: 0.19942

COMPARATIVE CONTEXT:
• Global Average at Age 81: -2.1 years
• Regional Rank: Top 25 globally
• Historical Trend: Stable

Based on 255,153 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.5%.

Human: What is the life expectancy for a 81 year old female in USA as of 2024?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: USA
• Age: 81 years
• Sex: Female
• Reference Year: 2024

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 81 (e_81): 4.5 years
• Expected Age at Death: 85.5 years
• Median Survival Time: 3.1 years
• Modal Age at Death: 80.5 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_81): 40.5%
• 10-Year Survival (₁₀p_81): 16.4%
• 20-Year Survival (₂₀p_81): 2.7%

MORTALITY METRICS:
• Force of Mortality (μ_81): 0.18079
• Probability of Death within 1 Year (q_81): 0.16539
• Hazard Rate: 0.19942

COMPARATIVE CONTEXT:
• Global Average at Age 81: -2.1 years
• Regional Rank: Top 25 globally
• Historical Trend: Stable

Based on 255,153 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.5%.


Instruction: Show survival curve for Germany female in 2019

Response:
SURVIVAL CURVE ANALYSIS

Population: Germany Female
Reference Year: 2019
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         75.8
    1          99,997            9         0.00009         80.8
    5          99,988           25         0.00025         76.6
   10          99,963           67         0.00067         73.9
   20          99,896           89         0.00089         62.0
   30          99,807          153         0.00153         47.3
   40          99,654          288         0.00289         37.7
   50          99,366          495         0.00498         27.6
   60          98,871          706         0.00714         18.9
   70          98,165          865         0.00881          5.1
   80          97,300        1,201         0.01234          0.0
   90          96,099        2,035         0.02118          2.2
  100          94,064        3,263         0.03469          4.1
  110          90,801       90,801         1.00000          2.0

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 84.9 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.3%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.81

The survival curve follows Gompertz law after age 30.
Data sourced from 150,720 death certificates.

Human: Show survival curve for Germany female in 2019

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Germany Female
Reference Year: 2019
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         75.8
    1          99,997            9         0.00009         80.8
    5          99,988           25         0.00025         76.6
   10          99,963           67         0.00067         73.9
   20          99,896           89         0.00089         62.0
   30          99,807          153         0.00153         47.3
   40          99,654          288         0.00289         37.7
   50          99,366          495         0.00498         27.6
   60          98,871          706         0.00714         18.9
   70          98,165          865         0.00881          5.1
   80          97,300        1,201         0.01234          0.0
   90          96,099        2,035         0.02118          2.2
  100          94,064        3,263         0.03469          4.1
  110          90,801       90,801         1.00000          2.0

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 84.9 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.3%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.81

The survival curve follows Gompertz law after age 30.
Data sourced from 150,720 death certificates.


Instruction: Compare maternal mortality between USA, South Korea and UK

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: USA, South Korea, UK
Reference Year: 2021

COMPARATIVE STATISTICS:
• USA: 29.4 per 100,000 live births
• South Korea: 3.2 per 100,000 live births
• UK: 41.3 per 100,000 live births

RANKINGS:
1. South Korea: 3.2
2. USA: 29.4
3. UK: 41.3

STATISTICAL ANALYSIS:
• Range: 38.1
• Mean: 24.7
• Median: 29.4
• Standard Deviation: 15.9
• Coefficient of Variation: 64.5%

RELATIVE COMPARISONS:
• Best vs Worst: 12.79x difference
• Above Average: 2/3
• Global Ranking: USA: #115, South Korea: #38, UK: #145

CONTRIBUTING FACTORS:
• Healthcare System: 24% of variation
• Economic Development: 27% of variation
• Public Health Policy: 12% of variation
• Demographics: 13% of variation
• Environmental Factors: 8% of variation

Convergence/Divergence: Converging at 1.3% annually

Human: Compare maternal mortality between USA, South Korea and UK

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: USA, South Korea, UK
Reference Year: 2021

COMPARATIVE STATISTICS:
• USA: 29.4 per 100,000 live births
• South Korea: 3.2 per 100,000 live births
• UK: 41.3 per 100,000 live births

RANKINGS:
1. South Korea: 3.2
2. USA: 29.4
3. UK: 41.3

STATISTICAL ANALYSIS:
• Range: 38.1
• Mean: 24.7
• Median: 29.4
• Standard Deviation: 15.9
• Coefficient of Variation: 64.5%

RELATIVE COMPARISONS:
• Best vs Worst: 12.79x difference
• Above Average: 2/3
• Global Ranking: USA: #115, South Korea: #38, UK: #145

CONTRIBUTING FACTORS:
• Healthcare System: 24% of variation
• Economic Development: 27% of variation
• Public Health Policy: 12% of variation
• Demographics: 13% of variation
• Environmental Factors: 8% of variation

Convergence/Divergence: Converging at 1.3% annually


Instruction: Compare maternal mortality between Japan, India, Russia, Australia and UK

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: Japan, India, Russia, Australia, UK
Reference Year: 2022

COMPARATIVE STATISTICS:
• Japan: 38.8 per 100,000 live births
• India: 10.4 per 100,000 live births
• Russia: 19.5 per 100,000 live births
• Australia: 35.1 per 100,000 live births
• UK: 34.6 per 100,000 live births

RANKINGS:
1. India: 10.4
2. Russia: 19.5
3. UK: 34.6
4. Australia: 35.1
5. Japan: 38.8

STATISTICAL ANALYSIS:
• Range: 28.4
• Mean: 27.7
• Median: 34.6
• Standard Deviation: 10.9
• Coefficient of Variation: 39.3%

RELATIVE COMPARISONS:
• Best vs Worst: 3.74x difference
• Above Average: 3/5
• Global Ranking: Japan: #159, India: #75, Russia: #43

CONTRIBUTING FACTORS:
• Healthcare System: 24% of variation
• Economic Development: 22% of variation
• Public Health Policy: 24% of variation
• Demographics: 17% of variation
• Environmental Factors: 10% of variation

Convergence/Divergence: Diverging at 1.9% annually

Human: Compare maternal mortality between Japan, India, Russia, Australia and UK

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: Japan, India, Russia, Australia, UK
Reference Year: 2022

COMPARATIVE STATISTICS:
• Japan: 38.8 per 100,000 live births
• India: 10.4 per 100,000 live births
• Russia: 19.5 per 100,000 live births
• Australia: 35.1 per 100,000 live births
• UK: 34.6 per 100,000 live births

RANKINGS:
1. India: 10.4
2. Russia: 19.5
3. UK: 34.6
4. Australia: 35.1
5. Japan: 38.8

STATISTICAL ANALYSIS:
• Range: 28.4
• Mean: 27.7
• Median: 34.6
• Standard Deviation: 10.9
• Coefficient of Variation: 39.3%

RELATIVE COMPARISONS:
• Best vs Worst: 3.74x difference
• Above Average: 3/5
• Global Ranking: Japan: #159, India: #75, Russia: #43

CONTRIBUTING FACTORS:
• Healthcare System: 24% of variation
• Economic Development: 22% of variation
• Public Health Policy: 24% of variation
• Demographics: 17% of variation
• Environmental Factors: 10% of variation

Convergence/Divergence: Diverging at 1.9% annually


Instruction: What is the mortality rate for Hypertension in France for 45-64 in 2024?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Hypertension
Location: France
Year: 2024
Age Group: 45-64

MORTALITY STATISTICS:
• Crude Death Rate: 11.2 per 100,000 population
• Age-Adjusted Rate: 9.8 per 100,000
• Total Deaths: 551,837
• Percentage of All Deaths: 22.0%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 13.5 per 100,000
• Female Death Rate: 9.6 per 100,000
• Sex Ratio (M:F): 1.33:1

TREND ANALYSIS:
• 5-Year Change: +10.1%
• 10-Year Change: -6.9%
• Annual Percentage Change: +1.8%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #9
• Years of Potential Life Lost (YPLL): 12955577
• Economic Burden: $63.3 billion annually
• Preventable Deaths: 54%

RISK FACTORS:
• Multiple factors
• Age-dependent
• Varies by population

International Classification of Diseases (ICD-10): I10-I15
Data Quality: Complete (88% coverage)

Human: What is the mortality rate for Hypertension in France for 45-64 in 2024?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Hypertension
Location: France
Year: 2024
Age Group: 45-64

MORTALITY STATISTICS:
• Crude Death Rate: 11.2 per 100,000 population
• Age-Adjusted Rate: 9.8 per 100,000
• Total Deaths: 551,837
• Percentage of All Deaths: 22.0%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 13.5 per 100,000
• Female Death Rate: 9.6 per 100,000
• Sex Ratio (M:F): 1.33:1

TREND ANALYSIS:
• 5-Year Change: +10.1%
• 10-Year Change: -6.9%
• Annual Percentage Change: +1.8%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #9
• Years of Potential Life Lost (YPLL): 12955577
• Economic Burden: $63.3 billion annually
• Preventable Deaths: 54%

RISK FACTORS:
• Multiple factors
• Age-dependent
• Varies by population

International Classification of Diseases (ICD-10): I10-I15
Data Quality: Complete (88% coverage)


Instruction: Analyze mortality differences by marital status in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Marital Status
Country: USA
Analysis Period: 2022

MORTALITY RATES BY MARITAL STATUS (per 100,000):
• Married: 755.3
• Single: 1157.7
• Divorced: 1041.0
• Widowed: 503.1

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.19
• Rate Difference: 639.8 per 100,000
• Population Attributable Risk: 19.4%
• Gini Coefficient: 0.296

LIFE EXPECTANCY BY MARITAL STATUS:
• Married: 79.3 years
• Single: 82.2 years
• Divorced: 84.0 years
• Widowed: 74.4 years

CONTRIBUTING FACTORS:
• Healthcare Access: 31% of disparity
• Socioeconomic Status: 29% of disparity
• Environmental Factors: 18% of disparity
• Behavioral Factors: 15% of disparity
• Biological Factors: 15% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: +1.5%

Social determinants explain 67% of observed mortality differences.

Human: Analyze mortality differences by marital status in the USA

Actuarial AI: DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Marital Status
Country: USA
Analysis Period: 2022

MORTALITY RATES BY MARITAL STATUS (per 100,000):
• Married: 755.3
• Single: 1157.7
• Divorced: 1041.0
• Widowed: 503.1

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.19
• Rate Difference: 639.8 per 100,000
• Population Attributable Risk: 19.4%
• Gini Coefficient: 0.296

LIFE EXPECTANCY BY MARITAL STATUS:
• Married: 79.3 years
• Single: 82.2 years
• Divorced: 84.0 years
• Widowed: 74.4 years

CONTRIBUTING FACTORS:
• Healthcare Access: 31% of disparity
• Socioeconomic Status: 29% of disparity
• Environmental Factors: 18% of disparity
• Behavioral Factors: 15% of disparity
• Biological Factors: 15% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: +1.5%

Social determinants explain 67% of observed mortality differences.


Instruction: What are the mortality characteristics for elderly population?

Response:
AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Elderly (65+ years)

MORTALITY METRICS:
• Death Rate: 11.36 per 1,000
• Leading Causes: Heart disease, cancer, Alzheimer's
• Preventable Deaths: 38%

Life table analysis shows stable risk profile.

Human: What are the mortality characteristics for elderly population?

Actuarial AI: AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Elderly (65+ years)

MORTALITY METRICS:
• Death Rate: 11.36 per 1,000
• Leading Causes: Heart disease, cancer, Alzheimer's
• Preventable Deaths: 38%

Life table analysis shows stable risk profile.


Instruction: Summarize individual life mortality experience study results

Response:
MORTALITY EXPERIENCE STUDY

Study Type: Individual Life Insurance
Study Period: 2021-2024
Exposure: 439884 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 1.11
• Deaths Actual: 7,442
• Deaths Expected: 3,652

BY DURATION:
• Select Period (Years 1-5): 0.73
• Ultimate (Years 6+): 1.06

Statistical confidence: 95% CI [0.84, 1.09]

Human: Summarize individual life mortality experience study results

Actuarial AI: MORTALITY EXPERIENCE STUDY

Study Type: Individual Life Insurance
Study Period: 2021-2024
Exposure: 439884 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 1.11
• Deaths Actual: 7,442
• Deaths Expected: 3,652

BY DURATION:
• Select Period (Years 1-5): 0.73
• Ultimate (Years 6+): 1.06

Statistical confidence: 95% CI [0.84, 1.09]


Instruction: Calculate the 5-year death probability for a 22 year oldsmoker

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 22 years
• Assessment Period: 5 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_22): 0.000469 (0.0469%)
• 5-Year Death Probability (₍5₎q_22): 0.002341 (0.234%)
• Survival Probability (₍5₎p_22): 0.997659 (99.766%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_22): 0.000469
• Hazard Rate (h_22): 0.000469
• Cumulative Hazard (H_22): 0.002344
• Median Future Lifetime: 1478.4 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.5x standard
• Risk Category: Preferred Plus
• Insurability: Standard or better
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.001990
• Upper Bound: 0.002693

Analysis based on 115,765 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Calculate the 5-year death probability for a 22 year oldsmoker

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 22 years
• Assessment Period: 5 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_22): 0.000469 (0.0469%)
• 5-Year Death Probability (₍5₎q_22): 0.002341 (0.234%)
• Survival Probability (₍5₎p_22): 0.997659 (99.766%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_22): 0.000469
• Hazard Rate (h_22): 0.000469
• Cumulative Hazard (H_22): 0.002344
• Median Future Lifetime: 1478.4 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.5x standard
• Risk Category: Preferred Plus
• Insurability: Standard or better
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.001990
• Upper Bound: 0.002693

Analysis based on 115,765 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Calculate policy reserve for 56 year old, 20-year term life, year 10

Response:
POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 46
• Current Age: 56
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $665.31
• Present Value Future Benefits (PVFB): $57027.22
• Present Value Future Premiums (PVFP): $22093.02

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $32786.92
• Per $1,000 Face: $327.87

PROSPECTIVE METHOD:
• A₁_56:10⌉ = 0.1607
• ä_56:10⌉ = 8.4502
• ₁₀V = 100,000 × A₁ - P × ä = $32786.92

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10619.43
• Accumulated Cost of Insurance: $5751.98
• Interest Earned: $1889.29
• ₁₀V = $32786.92

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $31147.58
• Tax Reserve: $30163.97
• GAAP Reserve: $34426.27

Human: Calculate policy reserve for 56 year old, 20-year term life, year 10

Actuarial AI: POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 46
• Current Age: 56
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $665.31
• Present Value Future Benefits (PVFB): $57027.22
• Present Value Future Premiums (PVFP): $22093.02

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $32786.92
• Per $1,000 Face: $327.87

PROSPECTIVE METHOD:
• A₁_56:10⌉ = 0.1607
• ä_56:10⌉ = 8.4502
• ₁₀V = 100,000 × A₁ - P × ä = $32786.92

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10619.43
• Accumulated Cost of Insurance: $5751.98
• Interest Earned: $1889.29
• ₁₀V = $32786.92

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $31147.58
• Tax Reserve: $30163.97
• GAAP Reserve: $34426.27


Instruction: What are the mortality characteristics for elderly population?

Response:
AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Elderly (65+ years)

MORTALITY METRICS:
• Death Rate: 17.58 per 1,000
• Leading Causes: Heart disease, cancer, Alzheimer's
• Preventable Deaths: 37%

Life table analysis shows stable risk profile.

Human: What are the mortality characteristics for elderly population?

Actuarial AI: AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Elderly (65+ years)

MORTALITY METRICS:
• Death Rate: 17.58 per 1,000
• Leading Causes: Heart disease, cancer, Alzheimer's
• Preventable Deaths: 37%

Life table analysis shows stable risk profile.


Instruction: Calculate policy reserve for 45 year old, 20-year term life, year 10

Response:
POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 35
• Current Age: 45
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1016.47
• Present Value Future Benefits (PVFB): $57639.50
• Present Value Future Premiums (PVFP): $30294.32

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $11208.02
• Per $1,000 Face: $112.08

PROSPECTIVE METHOD:
• A₁_45:10⌉ = 0.1609
• ä_45:10⌉ = 8.5669
• ₁₀V = 100,000 × A₁ - P × ä = $11208.02

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10881.81
• Accumulated Cost of Insurance: $5139.83
• Interest Earned: $1318.16
• ₁₀V = $11208.02

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $10647.62
• Tax Reserve: $10311.38
• GAAP Reserve: $11768.42

Human: Calculate policy reserve for 45 year old, 20-year term life, year 10

Actuarial AI: POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 35
• Current Age: 45
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1016.47
• Present Value Future Benefits (PVFB): $57639.50
• Present Value Future Premiums (PVFP): $30294.32

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $11208.02
• Per $1,000 Face: $112.08

PROSPECTIVE METHOD:
• A₁_45:10⌉ = 0.1609
• ä_45:10⌉ = 8.5669
• ₁₀V = 100,000 × A₁ - P × ä = $11208.02

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10881.81
• Accumulated Cost of Insurance: $5139.83
• Interest Earned: $1318.16
• ₁₀V = $11208.02

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $10647.62
• Tax Reserve: $10311.38
• GAAP Reserve: $11768.42


Instruction: What is the life expectancy for a 70 year old male in China as of 2022?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: China
• Age: 70 years
• Sex: Male
• Reference Year: 2022

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 70 (e_70): 7.2 years
• Expected Age at Death: 77.2 years
• Median Survival Time: 5.0 years
• Modal Age at Death: 72.2 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_70): 54.4%
• 10-Year Survival (₁₀p_70): 29.6%
• 20-Year Survival (₂₀p_70): 8.8%

MORTALITY METRICS:
• Force of Mortality (μ_70): 0.12178
• Probability of Death within 1 Year (q_70): 0.11465
• Hazard Rate: 0.12985

COMPARATIVE CONTEXT:
• Global Average at Age 70: 6.9 years
• Regional Rank: Top 40 globally
• Historical Trend: Improving

Based on 148,594 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.6%.

Human: What is the life expectancy for a 70 year old male in China as of 2022?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: China
• Age: 70 years
• Sex: Male
• Reference Year: 2022

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 70 (e_70): 7.2 years
• Expected Age at Death: 77.2 years
• Median Survival Time: 5.0 years
• Modal Age at Death: 72.2 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_70): 54.4%
• 10-Year Survival (₁₀p_70): 29.6%
• 20-Year Survival (₂₀p_70): 8.8%

MORTALITY METRICS:
• Force of Mortality (μ_70): 0.12178
• Probability of Death within 1 Year (q_70): 0.11465
• Hazard Rate: 0.12985

COMPARATIVE CONTEXT:
• Global Average at Age 70: 6.9 years
• Regional Rank: Top 40 globally
• Historical Trend: Improving

Based on 148,594 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.6%.


Instruction: Calculate Universal Life life insurance premium for 64 year old male, $250,000 coverage, Substandard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $250,000
• Duration: Lifetime Coverage
• Issue Age: 64
• Sex: Male
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_64): 0.007477
• Underwriting Multiplier: 1.5x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 69% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $3140.53
• Expense Charge: $785.13
• Reserve Accumulation: $1046.84
• Profit Margin: $261.71
• Gross Annual Premium: $5234.22

PAYMENT OPTIONS:
• Annual: $5234.22
• Semi-Annual: $2721.80 (x2 = $5443.59/year)
• Quarterly: $1387.07 (x4 = $5548.28/year)
• Monthly: $471.08 (x12 = $5652.96/year)

RESERVE CALCULATIONS:
• Net Level Premium: $3925.67
• First Year Reserve: $1046.84
• Terminal Reserve (Year 1): $113022.69

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Male
• Improvement Scale: MP-2019
• Select Period: 15 years
• Ultimate Mortality: CSO Male Ultimate

Internal Rate of Return: 11.9%
Profit Margin: 10.9%
Lapse Assumption: 6.1% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Universal Life life insurance premium for 64 year old male, $250,000 coverage, Substandard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $250,000
• Duration: Lifetime Coverage
• Issue Age: 64
• Sex: Male
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_64): 0.007477
• Underwriting Multiplier: 1.5x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 69% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $3140.53
• Expense Charge: $785.13
• Reserve Accumulation: $1046.84
• Profit Margin: $261.71
• Gross Annual Premium: $5234.22

PAYMENT OPTIONS:
• Annual: $5234.22
• Semi-Annual: $2721.80 (x2 = $5443.59/year)
• Quarterly: $1387.07 (x4 = $5548.28/year)
• Monthly: $471.08 (x12 = $5652.96/year)

RESERVE CALCULATIONS:
• Net Level Premium: $3925.67
• First Year Reserve: $1046.84
• Terminal Reserve (Year 1): $113022.69

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Male
• Improvement Scale: MP-2019
• Select Period: 15 years
• Ultimate Mortality: CSO Male Ultimate

Internal Rate of Return: 11.9%
Profit Margin: 10.9%
Lapse Assumption: 6.1% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Mortality risk assessment for 94 year old over next 5 years

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 94 years
• Assessment Period: 5 years
• Smoking Status: Non-smoker
• Health Conditions: hypertension, diabetes, heart disease

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_94): 0.005357 (0.5357%)
• 5-Year Death Probability (₍5₎q_94): 0.026501 (2.650%)
• Survival Probability (₍5₎p_94): 0.973499 (97.350%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_94): 0.005372
• Hazard Rate (h_94): 0.005372
• Cumulative Hazard (H_94): 0.026859
• Median Future Lifetime: 129.0 years

RISK CLASSIFICATION:
• Mortality Ratio: 5.4x standard
• Risk Category: Standard
• Insurability: Substandard with exclusions
• Recommended Premium Loading: 436%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.022526
• Upper Bound: 0.030476

Analysis based on 131,336 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Mortality risk assessment for 94 year old over next 5 years

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 94 years
• Assessment Period: 5 years
• Smoking Status: Non-smoker
• Health Conditions: hypertension, diabetes, heart disease

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_94): 0.005357 (0.5357%)
• 5-Year Death Probability (₍5₎q_94): 0.026501 (2.650%)
• Survival Probability (₍5₎p_94): 0.973499 (97.350%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_94): 0.005372
• Hazard Rate (h_94): 0.005372
• Cumulative Hazard (H_94): 0.026859
• Median Future Lifetime: 129.0 years

RISK CLASSIFICATION:
• Mortality Ratio: 5.4x standard
• Risk Category: Standard
• Insurability: Substandard with exclusions
• Recommended Premium Loading: 436%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.022526
• Upper Bound: 0.030476

Analysis based on 131,336 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: What is the mortality rate for Cancer in France for 25-44 in 2024?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Cancer
Location: France
Year: 2024
Age Group: 25-44

MORTALITY STATISTICS:
• Crude Death Rate: 162.3 per 100,000 population
• Age-Adjusted Rate: 151.1 per 100,000
• Total Deaths: 852,318
• Percentage of All Deaths: 3.6%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 194.8 per 100,000
• Female Death Rate: 138.0 per 100,000
• Sex Ratio (M:F): 1.37:1

TREND ANALYSIS:
• 5-Year Change: +3.7%
• 10-Year Change: +15.2%
• Annual Percentage Change: +2.2%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #7
• Years of Potential Life Lost (YPLL): 22309193
• Economic Burden: $24.6 billion annually
• Preventable Deaths: 22%

RISK FACTORS:
• Tobacco use: 30% attributable
• Diet: 20%
• Infections: 15%
• Alcohol: 10%
• Environmental: 10%

International Classification of Diseases (ICD-10): C00-C97
Data Quality: Complete (94% coverage)

Human: What is the mortality rate for Cancer in France for 25-44 in 2024?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Cancer
Location: France
Year: 2024
Age Group: 25-44

MORTALITY STATISTICS:
• Crude Death Rate: 162.3 per 100,000 population
• Age-Adjusted Rate: 151.1 per 100,000
• Total Deaths: 852,318
• Percentage of All Deaths: 3.6%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 194.8 per 100,000
• Female Death Rate: 138.0 per 100,000
• Sex Ratio (M:F): 1.37:1

TREND ANALYSIS:
• 5-Year Change: +3.7%
• 10-Year Change: +15.2%
• Annual Percentage Change: +2.2%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #7
• Years of Potential Life Lost (YPLL): 22309193
• Economic Burden: $24.6 billion annually
• Preventable Deaths: 22%

RISK FACTORS:
• Tobacco use: 30% attributable
• Diet: 20%
• Infections: 15%
• Alcohol: 10%
• Environmental: 10%

International Classification of Diseases (ICD-10): C00-C97
Data Quality: Complete (94% coverage)


Instruction: Calculate Universal Life life insurance premium for 24 year old female, $2,000,000 coverage, Standard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $2,000,000
• Duration: Lifetime Coverage
• Issue Age: 24
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_24): 0.000971
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 90% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $3263.35
• Expense Charge: $815.84
• Reserve Accumulation: $1087.78
• Profit Margin: $271.95
• Gross Annual Premium: $5438.92

PAYMENT OPTIONS:
• Annual: $5438.92
• Semi-Annual: $2828.24 (x2 = $5656.48/year)
• Quarterly: $1441.31 (x4 = $5765.26/year)
• Monthly: $489.50 (x12 = $5874.04/year)

RESERVE CALCULATIONS:
• Net Level Premium: $4079.19
• First Year Reserve: $1087.78
• Terminal Reserve (Year 41): $1337651.88

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2020
• Select Period: 20 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 11.9%
Profit Margin: 9.7%
Lapse Assumption: 3.5% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Universal Life life insurance premium for 24 year old female, $2,000,000 coverage, Standard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $2,000,000
• Duration: Lifetime Coverage
• Issue Age: 24
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_24): 0.000971
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 90% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $3263.35
• Expense Charge: $815.84
• Reserve Accumulation: $1087.78
• Profit Margin: $271.95
• Gross Annual Premium: $5438.92

PAYMENT OPTIONS:
• Annual: $5438.92
• Semi-Annual: $2828.24 (x2 = $5656.48/year)
• Quarterly: $1441.31 (x4 = $5765.26/year)
• Monthly: $489.50 (x12 = $5874.04/year)

RESERVE CALCULATIONS:
• Net Level Premium: $4079.19
• First Year Reserve: $1087.78
• Terminal Reserve (Year 41): $1337651.88

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2020
• Select Period: 20 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 11.9%
Profit Margin: 9.7%
Lapse Assumption: 3.5% annual

Illustration assumes guaranteed rates. Actual results may vary.