Instruction: What is the mortality rate for Cancer in UK for 65-74 in 2023?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Cancer
Location: UK
Year: 2023
Age Group: 65-74

MORTALITY STATISTICS:
• Crude Death Rate: 176.3 per 100,000 population
• Age-Adjusted Rate: 159.2 per 100,000
• Total Deaths: 3,427,644
• Percentage of All Deaths: 18.9%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 211.6 per 100,000
• Female Death Rate: 149.9 per 100,000
• Sex Ratio (M:F): 1.32:1

TREND ANALYSIS:
• 5-Year Change: +3.4%
• 10-Year Change: +8.8%
• Annual Percentage Change: +2.9%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #14
• Years of Potential Life Lost (YPLL): 94048224
• Economic Burden: $25.9 billion annually
• Preventable Deaths: 54%

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

International Classification of Diseases (ICD-10): C00-C97
Data Quality: Partial (88% coverage)

Human: What is the mortality rate for Cancer in UK for 65-74 in 2023?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Cancer
Location: UK
Year: 2023
Age Group: 65-74

MORTALITY STATISTICS:
• Crude Death Rate: 176.3 per 100,000 population
• Age-Adjusted Rate: 159.2 per 100,000
• Total Deaths: 3,427,644
• Percentage of All Deaths: 18.9%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 211.6 per 100,000
• Female Death Rate: 149.9 per 100,000
• Sex Ratio (M:F): 1.32:1

TREND ANALYSIS:
• 5-Year Change: +3.4%
• 10-Year Change: +8.8%
• Annual Percentage Change: +2.9%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #14
• Years of Potential Life Lost (YPLL): 94048224
• Economic Burden: $25.9 billion annually
• Preventable Deaths: 54%

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

International Classification of Diseases (ICD-10): C00-C97
Data Quality: Partial (88% coverage)


Instruction: What is the life expectancy for a 76 year old male in Australia as of 2017?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Australia
• Age: 76 years
• Sex: Male
• Reference Year: 2017

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 76 (e_76): 1.3 years
• Expected Age at Death: 77.3 years
• Median Survival Time: 0.9 years
• Modal Age at Death: 72.3 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_76): 10.9%
• 10-Year Survival (₁₀p_76): 1.2%
• 20-Year Survival (₂₀p_76): 0.0%

MORTALITY METRICS:
• Force of Mortality (μ_76): 0.44241
• Probability of Death within 1 Year (q_76): 0.35751
• Hazard Rate: 0.58413

COMPARATIVE CONTEXT:
• Global Average at Age 76: 6.9 years
• Regional Rank: Top 24 globally
• Historical Trend: Improving

Based on 351,634 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.4%.

Human: What is the life expectancy for a 76 year old male in Australia as of 2017?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Australia
• Age: 76 years
• Sex: Male
• Reference Year: 2017

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 76 (e_76): 1.3 years
• Expected Age at Death: 77.3 years
• Median Survival Time: 0.9 years
• Modal Age at Death: 72.3 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_76): 10.9%
• 10-Year Survival (₁₀p_76): 1.2%
• 20-Year Survival (₂₀p_76): 0.0%

MORTALITY METRICS:
• Force of Mortality (μ_76): 0.44241
• Probability of Death within 1 Year (q_76): 0.35751
• Hazard Rate: 0.58413

COMPARATIVE CONTEXT:
• Global Average at Age 76: 6.9 years
• Regional Rank: Top 24 globally
• Historical Trend: Improving

Based on 351,634 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.4%.


Instruction: Show survival curve for Germany male in 2015

Response:
SURVIVAL CURVE ANALYSIS

Population: Germany Male
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         81.8
    1          99,997           15         0.00015         81.5
    5          99,982           37         0.00037         77.7
   10          99,945           89         0.00089         67.8
   20          99,856          129         0.00129         56.4
   30          99,727          226         0.00227         45.9
   40          99,501          430         0.00432         36.4
   50          99,071          549         0.00554         34.2
   60          98,522          954         0.00968         18.8
   70          97,568        1,611         0.01651         13.1
   80          95,957        2,091         0.02179          1.3
   90          93,866        2,618         0.02789          3.9
  100          91,248        4,108         0.04502          3.5
  110          87,140       87,140         1.00000          3.3

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 83.0 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.5%
• Probability of Surviving to 80: 96.0%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 209,578 death certificates.

Human: Show survival curve for Germany male in 2015

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Germany Male
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         81.8
    1          99,997           15         0.00015         81.5
    5          99,982           37         0.00037         77.7
   10          99,945           89         0.00089         67.8
   20          99,856          129         0.00129         56.4
   30          99,727          226         0.00227         45.9
   40          99,501          430         0.00432         36.4
   50          99,071          549         0.00554         34.2
   60          98,522          954         0.00968         18.8
   70          97,568        1,611         0.01651         13.1
   80          95,957        2,091         0.02179          1.3
   90          93,866        2,618         0.02789          3.9
  100          91,248        4,108         0.04502          3.5
  110          87,140       87,140         1.00000          3.3

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 83.0 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.5%
• Probability of Surviving to 80: 96.0%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 209,578 death certificates.


Instruction: Analyze mortality patterns for 1940 birth cohort

Response:
BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1940
Current Age: 84 years
Cohort Size at Birth: 3,819,332

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 69.7 years
• Current Life Expectancy: 79.0 years
• Survival to Current Age: 84.0%

HISTORICAL EXPOSURES:
• World War II

MORTALITY PATTERN:
• Peak Infant Mortality: 39.2 per 1,000
• Current Mortality Rate: 9.9 per 1,000
• Improvement Since Birth: 48%

Cohort effects explain 16% of mortality variation.

Human: Analyze mortality patterns for 1940 birth cohort

Actuarial AI: BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1940
Current Age: 84 years
Cohort Size at Birth: 3,819,332

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 69.7 years
• Current Life Expectancy: 79.0 years
• Survival to Current Age: 84.0%

HISTORICAL EXPOSURES:
• World War II

MORTALITY PATTERN:
• Peak Infant Mortality: 39.2 per 1,000
• Current Mortality Rate: 9.9 per 1,000
• Improvement Since Birth: 48%

Cohort effects explain 16% of mortality variation.


Instruction: Calculate Term life insurance premium for 60 year old male, $5,000,000 coverage, 10 year term, Standard Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $5,000,000
• Term Length: 10 years
• Issue Age: 60
• Sex: Male
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_60): 0.003926
• Underwriting Multiplier: 0.9x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 66% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $11779.34
• Expense Charge: $2944.83
• Reserve Accumulation: $3926.45
• Profit Margin: $981.61
• Gross Annual Premium: $19632.23

PAYMENT OPTIONS:
• Annual: $19632.23
• Semi-Annual: $10208.76 (x2 = $20417.52/year)
• Quarterly: $5202.54 (x4 = $20810.17/year)
• Monthly: $1766.90 (x12 = $21202.81/year)

RESERVE CALCULATIONS:
• Net Level Premium: $14724.17
• First Year Reserve: $3926.45
• Terminal Reserve (Year 10): $3060580.69

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Male
• Improvement Scale: MP-2020
• Select Period: 15 years
• Ultimate Mortality: CSO Male Ultimate

Internal Rate of Return: 11.4%
Profit Margin: 14.7%
Lapse Assumption: 6.1% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Term life insurance premium for 60 year old male, $5,000,000 coverage, 10 year term, Standard Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $5,000,000
• Term Length: 10 years
• Issue Age: 60
• Sex: Male
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_60): 0.003926
• Underwriting Multiplier: 0.9x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 66% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $11779.34
• Expense Charge: $2944.83
• Reserve Accumulation: $3926.45
• Profit Margin: $981.61
• Gross Annual Premium: $19632.23

PAYMENT OPTIONS:
• Annual: $19632.23
• Semi-Annual: $10208.76 (x2 = $20417.52/year)
• Quarterly: $5202.54 (x4 = $20810.17/year)
• Monthly: $1766.90 (x12 = $21202.81/year)

RESERVE CALCULATIONS:
• Net Level Premium: $14724.17
• First Year Reserve: $3926.45
• Terminal Reserve (Year 10): $3060580.69

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Male
• Improvement Scale: MP-2020
• Select Period: 15 years
• Ultimate Mortality: CSO Male Ultimate

Internal Rate of Return: 11.4%
Profit Margin: 14.7%
Lapse Assumption: 6.1% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: What is the life expectancy for a 41 year old both in India as of 2019?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: India
• Age: 41 years
• Sex: Both
• Reference Year: 2019

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 41 (e_41): 25.0 years
• Expected Age at Death: 66.0 years
• Median Survival Time: 17.3 years
• Modal Age at Death: 61.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_41): 82.5%
• 10-Year Survival (₁₀p_41): 68.1%
• 20-Year Survival (₂₀p_41): 46.3%

MORTALITY METRICS:
• Force of Mortality (μ_41): 0.03846
• Probability of Death within 1 Year (q_41): 0.03773
• Hazard Rate: 0.03922

COMPARATIVE CONTEXT:
• Global Average at Age 41: 28.7 years
• Regional Rank: Top 20 globally
• Historical Trend: Improving

Based on 262,935 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.9%.

Human: What is the life expectancy for a 41 year old both in India as of 2019?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: India
• Age: 41 years
• Sex: Both
• Reference Year: 2019

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 41 (e_41): 25.0 years
• Expected Age at Death: 66.0 years
• Median Survival Time: 17.3 years
• Modal Age at Death: 61.0 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_41): 82.5%
• 10-Year Survival (₁₀p_41): 68.1%
• 20-Year Survival (₂₀p_41): 46.3%

MORTALITY METRICS:
• Force of Mortality (μ_41): 0.03846
• Probability of Death within 1 Year (q_41): 0.03773
• Hazard Rate: 0.03922

COMPARATIVE CONTEXT:
• Global Average at Age 41: 28.7 years
• Regional Rank: Top 20 globally
• Historical Trend: Improving

Based on 262,935 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.9%.


Instruction: Calculate policy reserve for 61 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: 51
• Current Age: 61
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $875.87
• Present Value Future Benefits (PVFB): $48244.35
• Present Value Future Premiums (PVFP): $29808.49

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $27761.82
• Per $1,000 Face: $277.62

PROSPECTIVE METHOD:
• A₁_61:10⌉ = 0.2186
• ä_61:10⌉ = 9.6938
• ₁₀V = 100,000 × A₁ - P × ä = $27761.82

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9650.74
• Accumulated Cost of Insurance: $4545.05
• Interest Earned: $1825.95
• ₁₀V = $27761.82

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $26373.73
• Tax Reserve: $25540.87
• GAAP Reserve: $29149.91

Human: Calculate policy reserve for 61 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: 51
• Current Age: 61
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $875.87
• Present Value Future Benefits (PVFB): $48244.35
• Present Value Future Premiums (PVFP): $29808.49

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $27761.82
• Per $1,000 Face: $277.62

PROSPECTIVE METHOD:
• A₁_61:10⌉ = 0.2186
• ä_61:10⌉ = 9.6938
• ₁₀V = 100,000 × A₁ - P × ä = $27761.82

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9650.74
• Accumulated Cost of Insurance: $4545.05
• Interest Earned: $1825.95
• ₁₀V = $27761.82

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $26373.73
• Tax Reserve: $25540.87
• GAAP Reserve: $29149.91


Instruction: Summarize annuity mortality experience study results

Response:
MORTALITY EXPERIENCE STUDY

Study Type: Annuity Insurance
Study Period: 2020-2024
Exposure: 948427 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 1.09
• Deaths Actual: 5,095
• Deaths Expected: 3,918

BY DURATION:
• Select Period (Years 1-5): 0.82
• Ultimate (Years 6+): 1.01

Statistical confidence: 95% CI [0.93, 1.12]

Human: Summarize annuity mortality experience study results

Actuarial AI: MORTALITY EXPERIENCE STUDY

Study Type: Annuity Insurance
Study Period: 2020-2024
Exposure: 948427 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 1.09
• Deaths Actual: 5,095
• Deaths Expected: 3,918

BY DURATION:
• Select Period (Years 1-5): 0.82
• Ultimate (Years 6+): 1.01

Statistical confidence: 95% CI [0.93, 1.12]


Instruction: What is the probability of death within 10 years for someone age 47?

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 47 years
• Assessment Period: 10 years
• Smoking Status: Non-smoker
• Health Conditions: hypertension, cancer history, heart disease

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_47): 0.001607 (0.1607%)
• 10-Year Death Probability (₍10₎q_47): 0.015957 (1.596%)
• Survival Probability (₍10₎p_47): 0.984043 (98.404%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_47): 0.001609
• Hazard Rate (h_47): 0.001609
• Cumulative Hazard (H_47): 0.016086
• Median Future Lifetime: 430.9 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.6x standard
• Risk Category: Preferred
• Insurability: Substandard with exclusions
• Recommended Premium Loading: 61%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.013563
• Upper Bound: 0.018350

Analysis based on 97,132 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: What is the probability of death within 10 years for someone age 47?

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 47 years
• Assessment Period: 10 years
• Smoking Status: Non-smoker
• Health Conditions: hypertension, cancer history, heart disease

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_47): 0.001607 (0.1607%)
• 10-Year Death Probability (₍10₎q_47): 0.015957 (1.596%)
• Survival Probability (₍10₎p_47): 0.984043 (98.404%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_47): 0.001609
• Hazard Rate (h_47): 0.001609
• Cumulative Hazard (H_47): 0.016086
• Median Future Lifetime: 430.9 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.6x standard
• Risk Category: Preferred
• Insurability: Substandard with exclusions
• Recommended Premium Loading: 61%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.013563
• Upper Bound: 0.018350

Analysis based on 97,132 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


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

Response:
EXCESS MORTALITY ANALYSIS

Event: 2021 cold snap
Location: Brazil
Period: 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 50,872
• Observed Deaths: 56,909
• Excess Deaths: 6,037
• Excess Mortality Rate: 11.9%
• P-score: 11.9%
• Z-score: 5.85 (p < 0.001)

BASELINE CALCULATION:
• Method: 5-year average
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.7% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: -3.0% (603 deaths)
• 45-64 years: 13.9% (1,509 deaths)
• 65-74 years: 26.5% (1,509 deaths)
• 75+ years: 28.0% (2,414 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 3,751 (55%)
• Indirect (probable): 730 (22%)
• Collateral (delayed care): 1,029 (17%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [5,131, 6,942]
• Probability of chance: < 0.001
• Power: 0.95

Years of Life Lost: 63128
Economic Impact: $8.6 billion
Quality-Adjusted Life Years Lost: 51884

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

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: 2021 cold snap
Location: Brazil
Period: 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 50,872
• Observed Deaths: 56,909
• Excess Deaths: 6,037
• Excess Mortality Rate: 11.9%
• P-score: 11.9%
• Z-score: 5.85 (p < 0.001)

BASELINE CALCULATION:
• Method: 5-year average
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.7% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: -3.0% (603 deaths)
• 45-64 years: 13.9% (1,509 deaths)
• 65-74 years: 26.5% (1,509 deaths)
• 75+ years: 28.0% (2,414 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 3,751 (55%)
• Indirect (probable): 730 (22%)
• Collateral (delayed care): 1,029 (17%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [5,131, 6,942]
• Probability of chance: < 0.001
• Power: 0.95

Years of Life Lost: 63128
Economic Impact: $8.6 billion
Quality-Adjusted Life Years Lost: 51884


Instruction: Calculate the 20-year death probability for a 48 year old

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 48 years
• Assessment Period: 20 years
• Smoking Status: Non-smoker
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_48): 0.000394 (0.0394%)
• 20-Year Death Probability (₍20₎q_48): 0.007853 (0.785%)
• Survival Probability (₍20₎p_48): 0.992147 (99.215%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_48): 0.000394
• Hazard Rate (h_48): 0.000394
• Cumulative Hazard (H_48): 0.007884
• Median Future Lifetime: 1758.5 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.4x standard
• Risk Category: Preferred Plus
• Insurability: Standard or better
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.006675
• Upper Bound: 0.009030

Analysis based on 97,890 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Calculate the 20-year death probability for a 48 year old

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 48 years
• Assessment Period: 20 years
• Smoking Status: Non-smoker
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_48): 0.000394 (0.0394%)
• 20-Year Death Probability (₍20₎q_48): 0.007853 (0.785%)
• Survival Probability (₍20₎p_48): 0.992147 (99.215%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_48): 0.000394
• Hazard Rate (h_48): 0.000394
• Cumulative Hazard (H_48): 0.007884
• Median Future Lifetime: 1758.5 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.4x standard
• Risk Category: Preferred Plus
• Insurability: Standard or better
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.006675
• Upper Bound: 0.009030

Analysis based on 97,890 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: What is the mortality rate for Suicide in USA in 2019?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Suicide
Location: USA
Year: 2019
Age Group: All ages

MORTALITY STATISTICS:
• Crude Death Rate: 15.6 per 100,000 population
• Age-Adjusted Rate: 14.6 per 100,000
• Total Deaths: 251,250
• Percentage of All Deaths: 19.1%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 18.7 per 100,000
• Female Death Rate: 13.2 per 100,000
• Sex Ratio (M:F): 1.49:1

TREND ANALYSIS:
• 5-Year Change: +6.2%
• 10-Year Change: -8.3%
• Annual Percentage Change: +1.7%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #8
• Years of Potential Life Lost (YPLL): 5200436
• Economic Burden: $52.2 billion annually
• Preventable Deaths: 41%

RISK FACTORS:
• Mental illness: 90% of cases
• Substance abuse: 30%
• Previous attempt: 40x risk
• Access to means: Critical
• Social isolation: 25%

International Classification of Diseases (ICD-10): X60-X84
Data Quality: Complete (91% coverage)

Human: What is the mortality rate for Suicide in USA in 2019?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Suicide
Location: USA
Year: 2019
Age Group: All ages

MORTALITY STATISTICS:
• Crude Death Rate: 15.6 per 100,000 population
• Age-Adjusted Rate: 14.6 per 100,000
• Total Deaths: 251,250
• Percentage of All Deaths: 19.1%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 18.7 per 100,000
• Female Death Rate: 13.2 per 100,000
• Sex Ratio (M:F): 1.49:1

TREND ANALYSIS:
• 5-Year Change: +6.2%
• 10-Year Change: -8.3%
• Annual Percentage Change: +1.7%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #8
• Years of Potential Life Lost (YPLL): 5200436
• Economic Burden: $52.2 billion annually
• Preventable Deaths: 41%

RISK FACTORS:
• Mental illness: 90% of cases
• Substance abuse: 30%
• Previous attempt: 40x risk
• Access to means: Critical
• Social isolation: 25%

International Classification of Diseases (ICD-10): X60-X84
Data Quality: Complete (91% coverage)


Instruction: What is the mortality rate for Diabetes in USA for 25-44 in 2022?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Diabetes
Location: USA
Year: 2022
Age Group: 25-44

MORTALITY STATISTICS:
• Crude Death Rate: 21.7 per 100,000 population
• Age-Adjusted Rate: 20.2 per 100,000
• Total Deaths: 511,989
• Percentage of All Deaths: 15.2%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 26.1 per 100,000
• Female Death Rate: 18.5 per 100,000
• Sex Ratio (M:F): 1.43:1

TREND ANALYSIS:
• 5-Year Change: -6.1%
• 10-Year Change: -12.7%
• Annual Percentage Change: +0.7%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #5
• Years of Potential Life Lost (YPLL): 7931479
• Economic Burden: $80.1 billion annually
• Preventable Deaths: 35%

RISK FACTORS:
• Obesity: 60% attributable
• Physical inactivity: 30%
• Diet: 40%
• Genetics: 25%
• Age: Progressive

International Classification of Diseases (ICD-10): E10-E14
Data Quality: Partial (92% coverage)

Human: What is the mortality rate for Diabetes in USA for 25-44 in 2022?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Diabetes
Location: USA
Year: 2022
Age Group: 25-44

MORTALITY STATISTICS:
• Crude Death Rate: 21.7 per 100,000 population
• Age-Adjusted Rate: 20.2 per 100,000
• Total Deaths: 511,989
• Percentage of All Deaths: 15.2%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 26.1 per 100,000
• Female Death Rate: 18.5 per 100,000
• Sex Ratio (M:F): 1.43:1

TREND ANALYSIS:
• 5-Year Change: -6.1%
• 10-Year Change: -12.7%
• Annual Percentage Change: +0.7%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #5
• Years of Potential Life Lost (YPLL): 7931479
• Economic Burden: $80.1 billion annually
• Preventable Deaths: 35%

RISK FACTORS:
• Obesity: 60% attributable
• Physical inactivity: 30%
• Diet: 40%
• Genetics: 25%
• Age: Progressive

International Classification of Diseases (ICD-10): E10-E14
Data Quality: Partial (92% coverage)


Instruction: What is the probability of death within 30 years for someone age 54?

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 54 years
• Assessment Period: 30 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: diabetes, cancer history

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_54): 0.002740 (0.2740%)
• 30-Year Death Probability (₍30₎q_54): 0.079005 (7.900%)
• Survival Probability (₍30₎p_54): 0.920995 (92.100%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_54): 0.002743
• Hazard Rate (h_54): 0.002743
• Cumulative Hazard (H_54): 0.082301
• Median Future Lifetime: 252.7 years

RISK CLASSIFICATION:
• Mortality Ratio: 2.7x standard
• Risk Category: Standard Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 174%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.067154
• Upper Bound: 0.090856

Analysis based on 181,663 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: What is the probability of death within 30 years for someone age 54?

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 54 years
• Assessment Period: 30 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: diabetes, cancer history

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_54): 0.002740 (0.2740%)
• 30-Year Death Probability (₍30₎q_54): 0.079005 (7.900%)
• Survival Probability (₍30₎p_54): 0.920995 (92.100%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_54): 0.002743
• Hazard Rate (h_54): 0.002743
• Cumulative Hazard (H_54): 0.082301
• Median Future Lifetime: 252.7 years

RISK CLASSIFICATION:
• Mortality Ratio: 2.7x standard
• Risk Category: Standard Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 174%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.067154
• Upper Bound: 0.090856

Analysis based on 181,663 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: What is the probability of death within 30 years for someone age 19?

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 19 years
• Assessment Period: 30 years
• Smoking Status: Non-smoker
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_19): 0.000172 (0.0172%)
• 30-Year Death Probability (₍30₎q_19): 0.005150 (0.515%)
• Survival Probability (₍30₎p_19): 0.994850 (99.485%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_19): 0.000172
• Hazard Rate (h_19): 0.000172
• Cumulative Hazard (H_19): 0.005163
• Median Future Lifetime: 4027.4 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: 0.004377
• Upper Bound: 0.005922

Analysis based on 185,790 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: What is the probability of death within 30 years for someone age 19?

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 19 years
• Assessment Period: 30 years
• Smoking Status: Non-smoker
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_19): 0.000172 (0.0172%)
• 30-Year Death Probability (₍30₎q_19): 0.005150 (0.515%)
• Survival Probability (₍30₎p_19): 0.994850 (99.485%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_19): 0.000172
• Hazard Rate (h_19): 0.000172
• Cumulative Hazard (H_19): 0.005163
• Median Future Lifetime: 4027.4 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: 0.004377
• Upper Bound: 0.005922

Analysis based on 185,790 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Show survival curve for Canada female in 2018

Response:
SURVIVAL CURVE ANALYSIS

Population: Canada Female
Reference Year: 2018
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         75.0
    1          99,998           11         0.00011         77.5
    5          99,987           20         0.00020         70.2
   10          99,967           60         0.00060         71.3
   20          99,907          106         0.00106         60.8
   30          99,801          168         0.00168         47.2
   40          99,633          344         0.00345         38.4
   50          99,289          484         0.00487         26.3
   60          98,805          579         0.00586         18.0
   70          98,226        1,156         0.01177         12.7
   80          97,070        1,286         0.01325          2.4
   90          95,784        1,803         0.01882          4.3
  100          93,981        2,394         0.02547          2.7
  110          91,587       91,587         1.00000          2.6

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 75.3 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.8%
• Probability of Surviving to 80: 97.1%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 181,658 death certificates.

Human: Show survival curve for Canada female in 2018

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Canada Female
Reference Year: 2018
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         75.0
    1          99,998           11         0.00011         77.5
    5          99,987           20         0.00020         70.2
   10          99,967           60         0.00060         71.3
   20          99,907          106         0.00106         60.8
   30          99,801          168         0.00168         47.2
   40          99,633          344         0.00345         38.4
   50          99,289          484         0.00487         26.3
   60          98,805          579         0.00586         18.0
   70          98,226        1,156         0.01177         12.7
   80          97,070        1,286         0.01325          2.4
   90          95,784        1,803         0.01882          4.3
  100          93,981        2,394         0.02547          2.7
  110          91,587       91,587         1.00000          2.6

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 75.3 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.8%
• Probability of Surviving to 80: 97.1%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 181,658 death certificates.


Instruction: What is the probability of death within 5 years for someone age 60?

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 60 years
• Assessment Period: 5 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: diabetes, heart disease

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_60): 0.003930 (0.3930%)
• 5-Year Death Probability (₍5₎q_60): 0.019495 (1.949%)
• Survival Probability (₍5₎p_60): 0.980505 (98.051%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_60): 0.003937
• Hazard Rate (h_60): 0.003937
• Cumulative Hazard (H_60): 0.019687
• Median Future Lifetime: 176.0 years

RISK CLASSIFICATION:
• Mortality Ratio: 3.9x standard
• Risk Category: Standard Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 293%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.016571
• Upper Bound: 0.022419

Analysis based on 83,172 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 60?

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 60 years
• Assessment Period: 5 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: diabetes, heart disease

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_60): 0.003930 (0.3930%)
• 5-Year Death Probability (₍5₎q_60): 0.019495 (1.949%)
• Survival Probability (₍5₎p_60): 0.980505 (98.051%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_60): 0.003937
• Hazard Rate (h_60): 0.003937
• Cumulative Hazard (H_60): 0.019687
• Median Future Lifetime: 176.0 years

RISK CLASSIFICATION:
• Mortality Ratio: 3.9x standard
• Risk Category: Standard Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 293%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.016571
• Upper Bound: 0.022419

Analysis based on 83,172 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Compare urban vs other area mortality rates in Canada

Response:
GEOGRAPHIC MORTALITY ANALYSIS

Country: Canada
Focus: Urban Areas

MORTALITY RATES (per 100,000):
• Urban: 817.4
• Rural: 992.8
• Suburban: 762.3

Rural areas show 21.5% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.

Human: Compare urban vs other area mortality rates in Canada

Actuarial AI: GEOGRAPHIC MORTALITY ANALYSIS

Country: Canada
Focus: Urban Areas

MORTALITY RATES (per 100,000):
• Urban: 817.4
• Rural: 992.8
• Suburban: 762.3

Rural areas show 21.5% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.


Instruction: Calculate Whole Life life insurance premium for 66 year old male, $100,000 coverage, Standard Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $100,000
• Duration: Lifetime Coverage
• Issue Age: 66
• Sex: Male
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_66): 0.004796
• Underwriting Multiplier: 0.9x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 58% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1007.11
• Expense Charge: $251.78
• Reserve Accumulation: $335.70
• Profit Margin: $83.93
• Gross Annual Premium: $1678.52

PAYMENT OPTIONS:
• Annual: $1678.52
• Semi-Annual: $872.83 (x2 = $1745.66/year)
• Quarterly: $444.81 (x4 = $1779.23/year)
• Monthly: $151.07 (x12 = $1812.80/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1258.89
• First Year Reserve: $335.70
• Terminal Reserve (Year -1): $36644.62

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

Internal Rate of Return: 10.5%
Profit Margin: 13.8%
Lapse Assumption: 5.1% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Whole Life life insurance premium for 66 year old male, $100,000 coverage, Standard Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $100,000
• Duration: Lifetime Coverage
• Issue Age: 66
• Sex: Male
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_66): 0.004796
• Underwriting Multiplier: 0.9x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 58% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1007.11
• Expense Charge: $251.78
• Reserve Accumulation: $335.70
• Profit Margin: $83.93
• Gross Annual Premium: $1678.52

PAYMENT OPTIONS:
• Annual: $1678.52
• Semi-Annual: $872.83 (x2 = $1745.66/year)
• Quarterly: $444.81 (x4 = $1779.23/year)
• Monthly: $151.07 (x12 = $1812.80/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1258.89
• First Year Reserve: $335.70
• Terminal Reserve (Year -1): $36644.62

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

Internal Rate of Return: 10.5%
Profit Margin: 13.8%
Lapse Assumption: 5.1% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Project mortality rates for Germany in 2039

Response:
MORTALITY PROJECTION

Country: Germany
Target Year: 2039
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 533.7 per 100,000
• Life Expectancy: 85.8 years
• Annual Improvement: 1.97%

CONFIDENCE INTERVALS (95%):
• Lower: 453.6
• Upper: 613.8

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

Human: Project mortality rates for Germany in 2039

Actuarial AI: MORTALITY PROJECTION

Country: Germany
Target Year: 2039
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 533.7 per 100,000
• Life Expectancy: 85.8 years
• Annual Improvement: 1.97%

CONFIDENCE INTERVALS (95%):
• Lower: 453.6
• Upper: 613.8

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


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            2         0.00002         81.5
    1          99,998            9         0.00009         75.7
    5          99,989           27         0.00027         73.9
   10          99,962           62         0.00062         73.2
   20          99,900           89         0.00089         58.2
   30          99,811          194         0.00194         50.9
   40          99,617          353         0.00354         41.3
   50          99,264          395         0.00398         35.0
   60          98,869          576         0.00583         22.6
   70          98,293        1,138         0.01158          5.6
   80          97,155        1,177         0.01211          0.0
   90          95,978        1,622         0.01690          2.6
  100          94,356        2,565         0.02718          1.5
  110          91,791       91,791         1.00000          3.3

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 78.4 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.2%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 301,267 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            2         0.00002         81.5
    1          99,998            9         0.00009         75.7
    5          99,989           27         0.00027         73.9
   10          99,962           62         0.00062         73.2
   20          99,900           89         0.00089         58.2
   30          99,811          194         0.00194         50.9
   40          99,617          353         0.00354         41.3
   50          99,264          395         0.00398         35.0
   60          98,869          576         0.00583         22.6
   70          98,293        1,138         0.01158          5.6
   80          97,155        1,177         0.01211          0.0
   90          95,978        1,622         0.01690          2.6
  100          94,356        2,565         0.02718          1.5
  110          91,791       91,791         1.00000          3.3

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 78.4 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.2%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 301,267 death certificates.


Instruction: Calculate the 30-year death probability for a 95 year oldsmoker with heart disease, diabetes, obesity

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 95 years
• Assessment Period: 30 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: heart disease, diabetes, obesity

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_95): 0.015974 (1.5974%)
• 30-Year Death Probability (₍30₎q_95): 0.383121 (38.312%)
• Survival Probability (₍30₎p_95): 0.616879 (61.688%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_95): 0.016103
• Hazard Rate (h_95): 0.016102
• Cumulative Hazard (H_95): 0.483082
• Median Future Lifetime: 43.0 years

RISK CLASSIFICATION:
• Mortality Ratio: 16.0x standard
• Risk Category: Substandard
• Insurability: Substandard with exclusions
• Recommended Premium Loading: 1497%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.325653
• Upper Bound: 0.440589

Analysis based on 193,565 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Calculate the 30-year death probability for a 95 year oldsmoker with heart disease, diabetes, obesity

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 95 years
• Assessment Period: 30 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: heart disease, diabetes, obesity

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_95): 0.015974 (1.5974%)
• 30-Year Death Probability (₍30₎q_95): 0.383121 (38.312%)
• Survival Probability (₍30₎p_95): 0.616879 (61.688%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_95): 0.016103
• Hazard Rate (h_95): 0.016102
• Cumulative Hazard (H_95): 0.483082
• Median Future Lifetime: 43.0 years

RISK CLASSIFICATION:
• Mortality Ratio: 16.0x standard
• Risk Category: Substandard
• Insurability: Substandard with exclusions
• Recommended Premium Loading: 1497%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.325653
• Upper Bound: 0.440589

Analysis based on 193,565 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: 34.7 per 100,000 full-time workers
Annual Deaths: 1,249

LEADING CAUSES:
• Falls: 35%
• Struck by object: 24%
• Electrocution: 6%
• Caught-in/between: 19%

Workers' compensation death benefit: $441,523

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

Actuarial AI: OCCUPATIONAL MORTALITY ANALYSIS

Industry: Construction
Fatal Injury Rate: 34.7 per 100,000 full-time workers
Annual Deaths: 1,249

LEADING CAUSES:
• Falls: 35%
• Struck by object: 24%
• Electrocution: 6%
• Caught-in/between: 19%

Workers' compensation death benefit: $441,523


Instruction: Calculate policy reserve for 68 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: 58
• Current Age: 68
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1207.57
• Present Value Future Benefits (PVFB): $48003.14
• Present Value Future Premiums (PVFP): $35682.26

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $22068.89
• Per $1,000 Face: $220.69

PROSPECTIVE METHOD:
• A₁_68:10⌉ = 0.1617
• ä_68:10⌉ = 9.4528
• ₁₀V = 100,000 × A₁ - P × ä = $22068.89

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9021.57
• Accumulated Cost of Insurance: $3533.79
• Interest Earned: $1121.96
• ₁₀V = $22068.89

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $20965.45
• Tax Reserve: $20303.38
• GAAP Reserve: $23172.34

Human: Calculate policy reserve for 68 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: 58
• Current Age: 68
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1207.57
• Present Value Future Benefits (PVFB): $48003.14
• Present Value Future Premiums (PVFP): $35682.26

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $22068.89
• Per $1,000 Face: $220.69

PROSPECTIVE METHOD:
• A₁_68:10⌉ = 0.1617
• ä_68:10⌉ = 9.4528
• ₁₀V = 100,000 × A₁ - P × ä = $22068.89

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9021.57
• Accumulated Cost of Insurance: $3533.79
• Interest Earned: $1121.96
• ₁₀V = $22068.89

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $20965.45
• Tax Reserve: $20303.38
• GAAP Reserve: $23172.34


Instruction: Analyze mortality differences by occupation in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Occupation
Country: USA
Analysis Period: 2019

MORTALITY RATES BY OCCUPATION (per 100,000):
• Healthcare: 730.8
• Construction: 825.8
• Office: 879.6
• Transportation: 863.9
• Service: 464.4

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.39
• Rate Difference: 310.7 per 100,000
• Population Attributable Risk: 25.5%
• Gini Coefficient: 0.107

LIFE EXPECTANCY BY OCCUPATION:
• Healthcare: 72.4 years
• Construction: 74.2 years
• Office: 77.5 years
• Transportation: 72.7 years
• Service: 76.6 years

CONTRIBUTING FACTORS:
• Healthcare Access: 34% of disparity
• Socioeconomic Status: 24% of disparity
• Environmental Factors: 15% of disparity
• Behavioral Factors: 14% of disparity
• Biological Factors: 6% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: +1.3%

Social determinants explain 67% of observed mortality differences.

Human: Analyze mortality differences by occupation in the USA

Actuarial AI: DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Occupation
Country: USA
Analysis Period: 2019

MORTALITY RATES BY OCCUPATION (per 100,000):
• Healthcare: 730.8
• Construction: 825.8
• Office: 879.6
• Transportation: 863.9
• Service: 464.4

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.39
• Rate Difference: 310.7 per 100,000
• Population Attributable Risk: 25.5%
• Gini Coefficient: 0.107

LIFE EXPECTANCY BY OCCUPATION:
• Healthcare: 72.4 years
• Construction: 74.2 years
• Office: 77.5 years
• Transportation: 72.7 years
• Service: 76.6 years

CONTRIBUTING FACTORS:
• Healthcare Access: 34% of disparity
• Socioeconomic Status: 24% of disparity
• Environmental Factors: 15% of disparity
• Behavioral Factors: 14% of disparity
• Biological Factors: 6% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: +1.3%

Social determinants explain 67% of observed mortality differences.


Instruction: Calculate policy reserve for 65 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: 55
• Current Age: 65
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $677.43
• Present Value Future Benefits (PVFB): $42025.45
• Present Value Future Premiums (PVFP): $32606.31

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $27826.76
• Per $1,000 Face: $278.27

PROSPECTIVE METHOD:
• A₁_65:10⌉ = 0.2493
• ä_65:10⌉ = 9.8560
• ₁₀V = 100,000 × A₁ - P × ä = $27826.76

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10373.15
• Accumulated Cost of Insurance: $4617.36
• Interest Earned: $1401.05
• ₁₀V = $27826.76

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $26435.43
• Tax Reserve: $25600.62
• GAAP Reserve: $29218.10

Human: Calculate policy reserve for 65 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: 55
• Current Age: 65
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $677.43
• Present Value Future Benefits (PVFB): $42025.45
• Present Value Future Premiums (PVFP): $32606.31

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $27826.76
• Per $1,000 Face: $278.27

PROSPECTIVE METHOD:
• A₁_65:10⌉ = 0.2493
• ä_65:10⌉ = 9.8560
• ₁₀V = 100,000 × A₁ - P × ä = $27826.76

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10373.15
• Accumulated Cost of Insurance: $4617.36
• Interest Earned: $1401.05
• ₁₀V = $27826.76

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $26435.43
• Tax Reserve: $25600.62
• GAAP Reserve: $29218.10


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

Response:
OCCUPATIONAL MORTALITY ANALYSIS

Industry: Agriculture
Fatal Injury Rate: 142.0 per 100,000 full-time workers
Annual Deaths: 13,025

LEADING CAUSES:
• Falls: 25%
• Struck by object: 30%
• Electrocution: 13%
• Caught-in/between: 12%

Workers' compensation death benefit: $342,685

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

Actuarial AI: OCCUPATIONAL MORTALITY ANALYSIS

Industry: Agriculture
Fatal Injury Rate: 142.0 per 100,000 full-time workers
Annual Deaths: 13,025

LEADING CAUSES:
• Falls: 25%
• Struck by object: 30%
• Electrocution: 13%
• Caught-in/between: 12%

Workers' compensation death benefit: $342,685


Instruction: Show survival curve for Japan male in 2021

Response:
SURVIVAL CURVE ANALYSIS

Population: Japan Male
Reference Year: 2021
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         77.6
    1          99,997           16         0.00016         78.9
    5          99,981           30         0.00030         79.1
   10          99,951           77         0.00077         72.7
   20          99,874          156         0.00156         60.9
   30          99,718          285         0.00286         47.0
   40          99,433          383         0.00385         43.6
   50          99,050          657         0.00663         34.7
   60          98,393          774         0.00787         22.5
   70          97,619        1,561         0.01599          5.7
   80          96,058        2,319         0.02414          0.0
   90          93,739        2,697         0.02877          3.5
  100          91,042        3,623         0.03979          2.6
  110          87,419       87,419         1.00000          3.3

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 83.3 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.4%
• Probability of Surviving to 80: 96.1%

CURVE CHARACTERISTICS:
• Type: Type I (Rectangular)
• Compression: High
• Rectangularization Index: 0.72

The survival curve follows Gompertz law after age 30.
Data sourced from 283,611 death certificates.

Human: Show survival curve for Japan male in 2021

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Japan Male
Reference Year: 2021
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         77.6
    1          99,997           16         0.00016         78.9
    5          99,981           30         0.00030         79.1
   10          99,951           77         0.00077         72.7
   20          99,874          156         0.00156         60.9
   30          99,718          285         0.00286         47.0
   40          99,433          383         0.00385         43.6
   50          99,050          657         0.00663         34.7
   60          98,393          774         0.00787         22.5
   70          97,619        1,561         0.01599          5.7
   80          96,058        2,319         0.02414          0.0
   90          93,739        2,697         0.02877          3.5
  100          91,042        3,623         0.03979          2.6
  110          87,419       87,419         1.00000          3.3

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 83.3 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.4%
• Probability of Surviving to 80: 96.1%

CURVE CHARACTERISTICS:
• Type: Type I (Rectangular)
• Compression: High
• Rectangularization Index: 0.72

The survival curve follows Gompertz law after age 30.
Data sourced from 283,611 death certificates.


Instruction: Show survival curve for UK male in 2023

Response:
SURVIVAL CURVE ANALYSIS

Population: UK Male
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            3         0.00003         75.2
    1          99,997           12         0.00012         76.7
    5          99,985           31         0.00031         70.9
   10          99,954           65         0.00065         74.3
   20          99,889          133         0.00133         64.9
   30          99,756          265         0.00266         45.8
   40          99,491          397         0.00399         37.9
   50          99,094          647         0.00653         32.8
   60          98,447        1,034         0.01050         19.4
   70          97,413        1,415         0.01453          8.8
   80          95,998        1,629         0.01697          1.0
   90          94,369        2,665         0.02824          3.7
  100          91,704        3,215         0.03506          3.3
  110          88,489       88,489         1.00000          1.1

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 75.2 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.4%
• Probability of Surviving to 80: 96.0%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.74

The survival curve follows Gompertz law after age 30.
Data sourced from 437,422 death certificates.

Human: Show survival curve for UK male in 2023

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: UK Male
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            3         0.00003         75.2
    1          99,997           12         0.00012         76.7
    5          99,985           31         0.00031         70.9
   10          99,954           65         0.00065         74.3
   20          99,889          133         0.00133         64.9
   30          99,756          265         0.00266         45.8
   40          99,491          397         0.00399         37.9
   50          99,094          647         0.00653         32.8
   60          98,447        1,034         0.01050         19.4
   70          97,413        1,415         0.01453          8.8
   80          95,998        1,629         0.01697          1.0
   90          94,369        2,665         0.02824          3.7
  100          91,704        3,215         0.03506          3.3
  110          88,489       88,489         1.00000          1.1

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 75.2 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.4%
• Probability of Surviving to 80: 96.0%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.74

The survival curve follows Gompertz law after age 30.
Data sourced from 437,422 death certificates.


Instruction: Calculate mortality improvement factors for age 48

Response:
MORTALITY IMPROVEMENT ANALYSIS

Age: 48
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.17%
• Current (2024): 1.49%
• Ultimate (2044+): 0.88%

PROJECTION FACTORS:
• 10-Year Factor: 0.8608
• 20-Year Factor: 0.7411
• 30-Year Factor: 0.6379

Cohort effect adjustment: Applied
Gender-specific: No

Human: Calculate mortality improvement factors for age 48

Actuarial AI: MORTALITY IMPROVEMENT ANALYSIS

Age: 48
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.17%
• Current (2024): 1.49%
• Ultimate (2044+): 0.88%

PROJECTION FACTORS:
• 10-Year Factor: 0.8608
• 20-Year Factor: 0.7411
• 30-Year Factor: 0.6379

Cohort effect adjustment: Applied
Gender-specific: No


Instruction: Calculate Whole Life life insurance premium for 26 year old female, $1,000,000 coverage, Preferred rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $1,000,000
• Duration: Lifetime Coverage
• Issue Age: 26
• Sex: Female
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_26): 0.000779
• Underwriting Multiplier: 0.75x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 56% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1635.15
• Expense Charge: $408.79
• Reserve Accumulation: $545.05
• Profit Margin: $136.26
• Gross Annual Premium: $2725.25

PAYMENT OPTIONS:
• Annual: $2725.25
• Semi-Annual: $1417.13 (x2 = $2834.27/year)
• Quarterly: $722.19 (x4 = $2888.77/year)
• Monthly: $245.27 (x12 = $2943.28/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2043.94
• First Year Reserve: $545.05
• Terminal Reserve (Year 39): $405970.23

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2021
• Select Period: 20 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 9.5%
Profit Margin: 12.8%
Lapse Assumption: 3.2% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Whole Life life insurance premium for 26 year old female, $1,000,000 coverage, Preferred rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $1,000,000
• Duration: Lifetime Coverage
• Issue Age: 26
• Sex: Female
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_26): 0.000779
• Underwriting Multiplier: 0.75x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 56% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1635.15
• Expense Charge: $408.79
• Reserve Accumulation: $545.05
• Profit Margin: $136.26
• Gross Annual Premium: $2725.25

PAYMENT OPTIONS:
• Annual: $2725.25
• Semi-Annual: $1417.13 (x2 = $2834.27/year)
• Quarterly: $722.19 (x4 = $2888.77/year)
• Monthly: $245.27 (x12 = $2943.28/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2043.94
• First Year Reserve: $545.05
• Terminal Reserve (Year 39): $405970.23

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Female
• Improvement Scale: MP-2021
• Select Period: 20 years
• Ultimate Mortality: CSO Female Ultimate

Internal Rate of Return: 9.5%
Profit Margin: 12.8%
Lapse Assumption: 3.2% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate excess mortality during seasonal flu in UK for Q3 2021

Response:
EXCESS MORTALITY ANALYSIS

Event: seasonal flu
Location: UK
Period: Q3 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 80,605
• Observed Deaths: 115,185
• Excess Deaths: 34,580
• Excess Mortality Rate: 42.9%
• P-score: 42.9%
• Z-score: 3.52 (p < 0.001)

BASELINE CALCULATION:
• Method: Farrington surveillance
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 1.4% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 3.0% (3,458 deaths)
• 45-64 years: 19.0% (8,645 deaths)
• 65-74 years: 26.1% (8,645 deaths)
• 75+ years: 39.0% (13,832 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 24,258 (80%)
• Indirect (probable): 3,497 (23%)
• Collateral (delayed care): 5,736 (20%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [29,393, 39,767]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 363919
Economic Impact: $6.1 billion
Quality-Adjusted Life Years Lost: 353349

Human: Calculate excess mortality during seasonal flu in UK for Q3 2021

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: seasonal flu
Location: UK
Period: Q3 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 80,605
• Observed Deaths: 115,185
• Excess Deaths: 34,580
• Excess Mortality Rate: 42.9%
• P-score: 42.9%
• Z-score: 3.52 (p < 0.001)

BASELINE CALCULATION:
• Method: Farrington surveillance
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 1.4% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 3.0% (3,458 deaths)
• 45-64 years: 19.0% (8,645 deaths)
• 65-74 years: 26.1% (8,645 deaths)
• 75+ years: 39.0% (13,832 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 24,258 (80%)
• Indirect (probable): 3,497 (23%)
• Collateral (delayed care): 5,736 (20%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [29,393, 39,767]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 363919
Economic Impact: $6.1 billion
Quality-Adjusted Life Years Lost: 353349


Instruction: Calculate mortality improvement factors for age 80

Response:
MORTALITY IMPROVEMENT ANALYSIS

Age: 80
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.45%
• Current (2024): 0.60%
• Ultimate (2044+): 0.89%

PROJECTION FACTORS:
• 10-Year Factor: 0.9417
• 20-Year Factor: 0.8869
• 30-Year Factor: 0.8352

Cohort effect adjustment: Not applied
Gender-specific: Yes

Human: Calculate mortality improvement factors for age 80

Actuarial AI: MORTALITY IMPROVEMENT ANALYSIS

Age: 80
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.45%
• Current (2024): 0.60%
• Ultimate (2044+): 0.89%

PROJECTION FACTORS:
• 10-Year Factor: 0.9417
• 20-Year Factor: 0.8869
• 30-Year Factor: 0.8352

Cohort effect adjustment: Not applied
Gender-specific: Yes


Instruction: What are the mortality characteristics for child population?

Response:
AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Child (1-12 years)

MORTALITY METRICS:
• Death Rate: 17.36 per 1,000
• Leading Causes: Accidents, cancer, congenital conditions
• Preventable Deaths: 35%

Life table analysis shows stable risk profile.

Human: What are the mortality characteristics for child population?

Actuarial AI: AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Child (1-12 years)

MORTALITY METRICS:
• Death Rate: 17.36 per 1,000
• Leading Causes: Accidents, cancer, congenital conditions
• Preventable Deaths: 35%

Life table analysis shows stable risk profile.


Instruction: Calculate Universal Life life insurance premium for 26 year old male, $500,000 coverage, Substandard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $500,000
• Duration: Lifetime Coverage
• Issue Age: 26
• Sex: Male
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_26): 0.002107
• Underwriting Multiplier: 1.5x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 72% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1769.81
• Expense Charge: $442.45
• Reserve Accumulation: $589.94
• Profit Margin: $147.48
• Gross Annual Premium: $2949.69

PAYMENT OPTIONS:
• Annual: $2949.69
• Semi-Annual: $1533.84 (x2 = $3067.68/year)
• Quarterly: $781.67 (x4 = $3126.67/year)
• Monthly: $265.47 (x12 = $3185.66/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2212.27
• First Year Reserve: $589.94
• Terminal Reserve (Year 39): $316450.73

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

Internal Rate of Return: 8.8%
Profit Margin: 9.0%
Lapse Assumption: 5.7% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Universal Life life insurance premium for 26 year old male, $500,000 coverage, Substandard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $500,000
• Duration: Lifetime Coverage
• Issue Age: 26
• Sex: Male
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_26): 0.002107
• Underwriting Multiplier: 1.5x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 72% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1769.81
• Expense Charge: $442.45
• Reserve Accumulation: $589.94
• Profit Margin: $147.48
• Gross Annual Premium: $2949.69

PAYMENT OPTIONS:
• Annual: $2949.69
• Semi-Annual: $1533.84 (x2 = $3067.68/year)
• Quarterly: $781.67 (x4 = $3126.67/year)
• Monthly: $265.47 (x12 = $3185.66/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2212.27
• First Year Reserve: $589.94
• Terminal Reserve (Year 39): $316450.73

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

Internal Rate of Return: 8.8%
Profit Margin: 9.0%
Lapse Assumption: 5.7% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate Universal Life life insurance premium for 51 year old male, $5,000,000 coverage, Preferred rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $5,000,000
• Duration: Lifetime Coverage
• Issue Age: 51
• Sex: Male
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_51): 0.002424
• Underwriting Multiplier: 0.75x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 95% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $20361.48
• Expense Charge: $5090.37
• Reserve Accumulation: $6787.16
• Profit Margin: $1696.79
• Gross Annual Premium: $33935.80

PAYMENT OPTIONS:
• Annual: $33935.80
• Semi-Annual: $17646.62 (x2 = $35293.23/year)
• Quarterly: $8992.99 (x4 = $35971.95/year)
• Monthly: $3054.22 (x12 = $36650.67/year)

RESERVE CALCULATIONS:
• Net Level Premium: $25451.85
• First Year Reserve: $6787.16
• Terminal Reserve (Year 14): $2062327.08

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Male
• Improvement Scale: MP-2021
• Select Period: 20 years
• Ultimate Mortality: CSO Male Ultimate

Internal Rate of Return: 9.2%
Profit Margin: 13.8%
Lapse Assumption: 4.8% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Universal Life life insurance premium for 51 year old male, $5,000,000 coverage, Preferred rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $5,000,000
• Duration: Lifetime Coverage
• Issue Age: 51
• Sex: Male
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_51): 0.002424
• Underwriting Multiplier: 0.75x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 95% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $20361.48
• Expense Charge: $5090.37
• Reserve Accumulation: $6787.16
• Profit Margin: $1696.79
• Gross Annual Premium: $33935.80

PAYMENT OPTIONS:
• Annual: $33935.80
• Semi-Annual: $17646.62 (x2 = $35293.23/year)
• Quarterly: $8992.99 (x4 = $35971.95/year)
• Monthly: $3054.22 (x12 = $36650.67/year)

RESERVE CALCULATIONS:
• Net Level Premium: $25451.85
• First Year Reserve: $6787.16
• Terminal Reserve (Year 14): $2062327.08

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Male
• Improvement Scale: MP-2021
• Select Period: 20 years
• Ultimate Mortality: CSO Male Ultimate

Internal Rate of Return: 9.2%
Profit Margin: 13.8%
Lapse Assumption: 4.8% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Compare life expectancy between Australia, India and Italy

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Life Expectancy
Countries: Australia, India, Italy
Reference Year: 2021

COMPARATIVE STATISTICS:
• Australia: 80.4 years
• India: 80.8 years
• Italy: 74.3 years

RANKINGS:
1. India: 80.8
2. Australia: 80.4
3. Italy: 74.3

STATISTICAL ANALYSIS:
• Range: 6.6
• Mean: 78.5
• Median: 80.4
• Standard Deviation: 3.0
• Coefficient of Variation: 3.8%

RELATIVE COMPARISONS:
• Best vs Worst: 0.92x difference
• Above Average: 2/3
• Global Ranking: Australia: #139, India: #9, Italy: #117

CONTRIBUTING FACTORS:
• Healthcare System: 29% of variation
• Economic Development: 25% of variation
• Public Health Policy: 14% of variation
• Demographics: 12% of variation
• Environmental Factors: 14% of variation

Convergence/Divergence: Converging at 1.8% annually

Human: Compare life expectancy between Australia, India and Italy

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Life Expectancy
Countries: Australia, India, Italy
Reference Year: 2021

COMPARATIVE STATISTICS:
• Australia: 80.4 years
• India: 80.8 years
• Italy: 74.3 years

RANKINGS:
1. India: 80.8
2. Australia: 80.4
3. Italy: 74.3

STATISTICAL ANALYSIS:
• Range: 6.6
• Mean: 78.5
• Median: 80.4
• Standard Deviation: 3.0
• Coefficient of Variation: 3.8%

RELATIVE COMPARISONS:
• Best vs Worst: 0.92x difference
• Above Average: 2/3
• Global Ranking: Australia: #139, India: #9, Italy: #117

CONTRIBUTING FACTORS:
• Healthcare System: 29% of variation
• Economic Development: 25% of variation
• Public Health Policy: 14% of variation
• Demographics: 12% of variation
• Environmental Factors: 14% of variation

Convergence/Divergence: Converging at 1.8% annually


Instruction: Calculate the 1-year death probability for a 33 year old with cancer history

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 33 years
• Assessment Period: 1 year
• Smoking Status: Non-smoker
• Health Conditions: cancer history

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_33): 0.000448 (0.0448%)
• 1-Year Death Probability (₍1₎q_33): 0.000448 (0.045%)
• Survival Probability (₍1₎p_33): 0.999552 (99.955%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_33): 0.000448
• Hazard Rate (h_33): 0.000448
• Cumulative Hazard (H_33): 0.000448
• Median Future Lifetime: 1546.2 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.4x standard
• Risk Category: Preferred Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.000381
• Upper Bound: 0.000515

Analysis based on 184,282 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Calculate the 1-year death probability for a 33 year old with cancer history

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 33 years
• Assessment Period: 1 year
• Smoking Status: Non-smoker
• Health Conditions: cancer history

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_33): 0.000448 (0.0448%)
• 1-Year Death Probability (₍1₎q_33): 0.000448 (0.045%)
• Survival Probability (₍1₎p_33): 0.999552 (99.955%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_33): 0.000448
• Hazard Rate (h_33): 0.000448
• Cumulative Hazard (H_33): 0.000448
• Median Future Lifetime: 1546.2 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.4x standard
• Risk Category: Preferred Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.000381
• Upper Bound: 0.000515

Analysis based on 184,282 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Summarize annuity mortality experience study results

Response:
MORTALITY EXPERIENCE STUDY

Study Type: Annuity Insurance
Study Period: 2019-2023
Exposure: 835626 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 0.88
• Deaths Actual: 2,805
• Deaths Expected: 6,030

BY DURATION:
• Select Period (Years 1-5): 0.88
• Ultimate (Years 6+): 0.99

Statistical confidence: 95% CI [0.89, 1.05]

Human: Summarize annuity mortality experience study results

Actuarial AI: MORTALITY EXPERIENCE STUDY

Study Type: Annuity Insurance
Study Period: 2019-2023
Exposure: 835626 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 0.88
• Deaths Actual: 2,805
• Deaths Expected: 6,030

BY DURATION:
• Select Period (Years 1-5): 0.88
• Ultimate (Years 6+): 0.99

Statistical confidence: 95% CI [0.89, 1.05]


Instruction: Calculate policy reserve for 59 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: 49
• Current Age: 59
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $537.36
• Present Value Future Benefits (PVFB): $50282.38
• Present Value Future Premiums (PVFP): $22551.76

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $19468.13
• Per $1,000 Face: $194.68

PROSPECTIVE METHOD:
• A₁_59:10⌉ = 0.2190
• ä_59:10⌉ = 9.7706
• ₁₀V = 100,000 × A₁ - P × ä = $19468.13

RETROSPECTIVE METHOD:
• Accumulated Premiums: $11799.29
• Accumulated Cost of Insurance: $3620.08
• Interest Earned: $1621.85
• ₁₀V = $19468.13

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $18494.72
• Tax Reserve: $17910.68
• GAAP Reserve: $20441.54

Human: Calculate policy reserve for 59 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: 49
• Current Age: 59
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $537.36
• Present Value Future Benefits (PVFB): $50282.38
• Present Value Future Premiums (PVFP): $22551.76

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $19468.13
• Per $1,000 Face: $194.68

PROSPECTIVE METHOD:
• A₁_59:10⌉ = 0.2190
• ä_59:10⌉ = 9.7706
• ₁₀V = 100,000 × A₁ - P × ä = $19468.13

RETROSPECTIVE METHOD:
• Accumulated Premiums: $11799.29
• Accumulated Cost of Insurance: $3620.08
• Interest Earned: $1621.85
• ₁₀V = $19468.13

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $18494.72
• Tax Reserve: $17910.68
• GAAP Reserve: $20441.54


Instruction: What is the life expectancy for a 15 year old male in USA as of 2018?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: USA
• Age: 15 years
• Sex: Male
• Reference Year: 2018

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 15 (e_15): 59.3 years
• Expected Age at Death: 74.3 years
• Median Survival Time: 41.1 years
• Modal Age at Death: 69.3 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_15): 92.0%
• 10-Year Survival (₁₀p_15): 84.7%
• 20-Year Survival (₂₀p_15): 71.8%

MORTALITY METRICS:
• Force of Mortality (μ_15): 0.01657
• Probability of Death within 1 Year (q_15): 0.01644
• Hazard Rate: 0.01671

COMPARATIVE CONTEXT:
• Global Average at Age 15: 63.9 years
• Regional Rank: Top 43 globally
• Historical Trend: Stable

Based on 473,714 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.7%.

Human: What is the life expectancy for a 15 year old male in USA as of 2018?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: USA
• Age: 15 years
• Sex: Male
• Reference Year: 2018

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 15 (e_15): 59.3 years
• Expected Age at Death: 74.3 years
• Median Survival Time: 41.1 years
• Modal Age at Death: 69.3 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_15): 92.0%
• 10-Year Survival (₁₀p_15): 84.7%
• 20-Year Survival (₂₀p_15): 71.8%

MORTALITY METRICS:
• Force of Mortality (μ_15): 0.01657
• Probability of Death within 1 Year (q_15): 0.01644
• Hazard Rate: 0.01671

COMPARATIVE CONTEXT:
• Global Average at Age 15: 63.9 years
• Regional Rank: Top 43 globally
• Historical Trend: Stable

Based on 473,714 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.7%.


Instruction: Calculate excess mortality during 2022 heat wave in Italy for Q3 2021

Response:
EXCESS MORTALITY ANALYSIS

Event: 2022 heat wave
Location: Italy
Period: Q3 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 92,398
• Observed Deaths: 119,992
• Excess Deaths: 27,594
• Excess Mortality Rate: 29.9%
• P-score: 29.9%
• Z-score: 3.75 (p < 0.001)

BASELINE CALCULATION:
• Method: Serfling regression
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 1.9% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 9.7% (2,759 deaths)
• 45-64 years: 6.3% (6,898 deaths)
• 65-74 years: 21.6% (6,898 deaths)
• 75+ years: 20.3% (11,037 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 16,642 (73%)
• Indirect (probable): 5,624 (23%)
• Collateral (delayed care): 5,116 (11%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [23,454, 31,733]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 289045
Economic Impact: $1.5 billion
Quality-Adjusted Life Years Lost: 261335

Human: Calculate excess mortality during 2022 heat wave in Italy for Q3 2021

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: 2022 heat wave
Location: Italy
Period: Q3 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 92,398
• Observed Deaths: 119,992
• Excess Deaths: 27,594
• Excess Mortality Rate: 29.9%
• P-score: 29.9%
• Z-score: 3.75 (p < 0.001)

BASELINE CALCULATION:
• Method: Serfling regression
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 1.9% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 9.7% (2,759 deaths)
• 45-64 years: 6.3% (6,898 deaths)
• 65-74 years: 21.6% (6,898 deaths)
• 75+ years: 20.3% (11,037 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 16,642 (73%)
• Indirect (probable): 5,624 (23%)
• Collateral (delayed care): 5,116 (11%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [23,454, 31,733]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 289045
Economic Impact: $1.5 billion
Quality-Adjusted Life Years Lost: 261335


Instruction: What is the mortality rate for Hypertension in France for Under 25 in 2022?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Hypertension
Location: France
Year: 2022
Age Group: Under 25

MORTALITY STATISTICS:
• Crude Death Rate: 11.9 per 100,000 population
• Age-Adjusted Rate: 11.3 per 100,000
• Total Deaths: 89,250
• Percentage of All Deaths: 23.7%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 14.3 per 100,000
• Female Death Rate: 10.2 per 100,000
• Sex Ratio (M:F): 1.24:1

TREND ANALYSIS:
• 5-Year Change: +14.0%
• 10-Year Change: -13.5%
• Annual Percentage Change: -3.0%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #4
• Years of Potential Life Lost (YPLL): 1315730
• Economic Burden: $99.6 billion annually
• Preventable Deaths: 35%

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

International Classification of Diseases (ICD-10): I10-I15
Data Quality: Near-Complete (91% coverage)

Human: What is the mortality rate for Hypertension in France for Under 25 in 2022?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Hypertension
Location: France
Year: 2022
Age Group: Under 25

MORTALITY STATISTICS:
• Crude Death Rate: 11.9 per 100,000 population
• Age-Adjusted Rate: 11.3 per 100,000
• Total Deaths: 89,250
• Percentage of All Deaths: 23.7%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 14.3 per 100,000
• Female Death Rate: 10.2 per 100,000
• Sex Ratio (M:F): 1.24:1

TREND ANALYSIS:
• 5-Year Change: +14.0%
• 10-Year Change: -13.5%
• Annual Percentage Change: -3.0%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #4
• Years of Potential Life Lost (YPLL): 1315730
• Economic Burden: $99.6 billion annually
• Preventable Deaths: 35%

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

International Classification of Diseases (ICD-10): I10-I15
Data Quality: Near-Complete (91% coverage)


Instruction: Calculate excess mortality during seasonal flu in Germany for Q4 2021

Response:
EXCESS MORTALITY ANALYSIS

Event: seasonal flu
Location: Germany
Period: Q4 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 37,552
• Observed Deaths: 54,542
• Excess Deaths: 16,990
• Excess Mortality Rate: 45.2%
• P-score: 45.2%
• Z-score: 5.87 (p < 0.001)

BASELINE CALCULATION:
• Method: Serfling regression
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.4% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: -4.5% (1,699 deaths)
• 45-64 years: 15.6% (4,247 deaths)
• 65-74 years: 20.0% (4,247 deaths)
• 75+ years: 39.7% (6,796 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 12,177 (80%)
• Indirect (probable): 4,430 (23%)
• Collateral (delayed care): 2,696 (20%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [14,441, 19,538]
• Probability of chance: < 0.001
• Power: 0.95

Years of Life Lost: 237999
Economic Impact: $2.9 billion
Quality-Adjusted Life Years Lost: 180933

Human: Calculate excess mortality during seasonal flu in Germany for Q4 2021

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: seasonal flu
Location: Germany
Period: Q4 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 37,552
• Observed Deaths: 54,542
• Excess Deaths: 16,990
• Excess Mortality Rate: 45.2%
• P-score: 45.2%
• Z-score: 5.87 (p < 0.001)

BASELINE CALCULATION:
• Method: Serfling regression
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.4% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: -4.5% (1,699 deaths)
• 45-64 years: 15.6% (4,247 deaths)
• 65-74 years: 20.0% (4,247 deaths)
• 75+ years: 39.7% (6,796 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 12,177 (80%)
• Indirect (probable): 4,430 (23%)
• Collateral (delayed care): 2,696 (20%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [14,441, 19,538]
• Probability of chance: < 0.001
• Power: 0.95

Years of Life Lost: 237999
Economic Impact: $2.9 billion
Quality-Adjusted Life Years Lost: 180933


Instruction: Show survival curve for Canada female in 2016

Response:
SURVIVAL CURVE ANALYSIS

Population: Canada Female
Reference Year: 2016
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         76.0
    1          99,998            9         0.00009         76.5
    5          99,989           20         0.00020         74.2
   10          99,969           60         0.00060         70.9
   20          99,909           91         0.00091         62.0
   30          99,818          164         0.00164         50.8
   40          99,654          261         0.00262         37.8
   50          99,393          538         0.00541         33.2
   60          98,855          755         0.00764         18.3
   70          98,100        1,060         0.01081          6.8
   80          97,040        1,286         0.01325          0.0
   90          95,754        2,080         0.02172          5.0
  100          93,674        2,256         0.02408          1.8
  110          91,418       91,418         1.00000          1.7

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 80.5 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.0%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 109,570 death certificates.

Human: Show survival curve for Canada female in 2016

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Canada Female
Reference Year: 2016
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         76.0
    1          99,998            9         0.00009         76.5
    5          99,989           20         0.00020         74.2
   10          99,969           60         0.00060         70.9
   20          99,909           91         0.00091         62.0
   30          99,818          164         0.00164         50.8
   40          99,654          261         0.00262         37.8
   50          99,393          538         0.00541         33.2
   60          98,855          755         0.00764         18.3
   70          98,100        1,060         0.01081          6.8
   80          97,040        1,286         0.01325          0.0
   90          95,754        2,080         0.02172          5.0
  100          93,674        2,256         0.02408          1.8
  110          91,418       91,418         1.00000          1.7

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 80.5 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.0%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 109,570 death certificates.


Instruction: Calculate Term life insurance premium for 53 year old female, $5,000,000 coverage, 15 year term, Standard Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $5,000,000
• Term Length: 15 years
• Issue Age: 53
• Sex: Female
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_53): 0.002298
• Underwriting Multiplier: 0.9x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 51% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $6894.56
• Expense Charge: $1723.64
• Reserve Accumulation: $2298.19
• Profit Margin: $574.55
• Gross Annual Premium: $11490.94

PAYMENT OPTIONS:
• Annual: $11490.94
• Semi-Annual: $5975.29 (x2 = $11950.57/year)
• Quarterly: $3045.10 (x4 = $12180.39/year)
• Monthly: $1034.18 (x12 = $12410.21/year)

RESERVE CALCULATIONS:
• Net Level Premium: $8618.20
• First Year Reserve: $2298.19
• Terminal Reserve (Year 15): $1697737.02

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

Internal Rate of Return: 11.5%
Profit Margin: 11.5%
Lapse Assumption: 5.4% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Term life insurance premium for 53 year old female, $5,000,000 coverage, 15 year term, Standard Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $5,000,000
• Term Length: 15 years
• Issue Age: 53
• Sex: Female
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_53): 0.002298
• Underwriting Multiplier: 0.9x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 51% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $6894.56
• Expense Charge: $1723.64
• Reserve Accumulation: $2298.19
• Profit Margin: $574.55
• Gross Annual Premium: $11490.94

PAYMENT OPTIONS:
• Annual: $11490.94
• Semi-Annual: $5975.29 (x2 = $11950.57/year)
• Quarterly: $3045.10 (x4 = $12180.39/year)
• Monthly: $1034.18 (x12 = $12410.21/year)

RESERVE CALCULATIONS:
• Net Level Premium: $8618.20
• First Year Reserve: $2298.19
• Terminal Reserve (Year 15): $1697737.02

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

Internal Rate of Return: 11.5%
Profit Margin: 11.5%
Lapse Assumption: 5.4% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate Universal Life life insurance premium for 20 year old male, $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: 20
• Sex: Male
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_20): 0.001150
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 72% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $3864.00
• Expense Charge: $966.00
• Reserve Accumulation: $1288.00
• Profit Margin: $322.00
• Gross Annual Premium: $6440.00

PAYMENT OPTIONS:
• Annual: $6440.00
• Semi-Annual: $3348.80 (x2 = $6697.60/year)
• Quarterly: $1706.60 (x4 = $6826.40/year)
• Monthly: $579.60 (x12 = $6955.20/year)

RESERVE CALCULATIONS:
• Net Level Premium: $4830.00
• First Year Reserve: $1288.00
• Terminal Reserve (Year 45): $1387903.71

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Male
• Improvement Scale: MP-2020
• Select Period: 25 years
• Ultimate Mortality: CSO Male Ultimate

Internal Rate of Return: 12.0%
Profit Margin: 13.0%
Lapse Assumption: 6.5% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Universal Life life insurance premium for 20 year old male, $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: 20
• Sex: Male
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_20): 0.001150
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 72% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $3864.00
• Expense Charge: $966.00
• Reserve Accumulation: $1288.00
• Profit Margin: $322.00
• Gross Annual Premium: $6440.00

PAYMENT OPTIONS:
• Annual: $6440.00
• Semi-Annual: $3348.80 (x2 = $6697.60/year)
• Quarterly: $1706.60 (x4 = $6826.40/year)
• Monthly: $579.60 (x12 = $6955.20/year)

RESERVE CALCULATIONS:
• Net Level Premium: $4830.00
• First Year Reserve: $1288.00
• Terminal Reserve (Year 45): $1387903.71

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Male
• Improvement Scale: MP-2020
• Select Period: 25 years
• Ultimate Mortality: CSO Male Ultimate

Internal Rate of Return: 12.0%
Profit Margin: 13.0%
Lapse Assumption: 6.5% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Project mortality rates for Japan in 2030

Response:
MORTALITY PROJECTION

Country: Japan
Target Year: 2030
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 540.0 per 100,000
• Life Expectancy: 83.7 years
• Annual Improvement: 1.93%

CONFIDENCE INTERVALS (95%):
• Lower: 459.0
• Upper: 621.0

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

Human: Project mortality rates for Japan in 2030

Actuarial AI: MORTALITY PROJECTION

Country: Japan
Target Year: 2030
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 540.0 per 100,000
• Life Expectancy: 83.7 years
• Annual Improvement: 1.93%

CONFIDENCE INTERVALS (95%):
• Lower: 459.0
• Upper: 621.0

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


Instruction: Analyze mortality differences by income in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Income
Country: USA
Analysis Period: 2019

MORTALITY RATES BY INCOME (per 100,000):
• <$25k: 696.5
• $25-50k: 1197.9
• $50-75k: 651.5
• $75-100k: 1188.7
• >$100k: 1075.1

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.44
• Rate Difference: 308.9 per 100,000
• Population Attributable Risk: 12.5%
• Gini Coefficient: 0.156

LIFE EXPECTANCY BY INCOME:
• <$25k: 84.7 years
• $25-50k: 78.2 years
• $50-75k: 78.4 years
• $75-100k: 72.5 years
• >$100k: 84.4 years

CONTRIBUTING FACTORS:
• Healthcare Access: 33% of disparity
• Socioeconomic Status: 22% of disparity
• Environmental Factors: 23% of disparity
• Behavioral Factors: 22% of disparity
• Biological Factors: 15% of disparity

TREND ANALYSIS:
• Disparities are widening
• Annual change in disparity: +1.6%

Social determinants explain 69% of observed mortality differences.

Human: Analyze mortality differences by income in the USA

Actuarial AI: DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Income
Country: USA
Analysis Period: 2019

MORTALITY RATES BY INCOME (per 100,000):
• <$25k: 696.5
• $25-50k: 1197.9
• $50-75k: 651.5
• $75-100k: 1188.7
• >$100k: 1075.1

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.44
• Rate Difference: 308.9 per 100,000
• Population Attributable Risk: 12.5%
• Gini Coefficient: 0.156

LIFE EXPECTANCY BY INCOME:
• <$25k: 84.7 years
• $25-50k: 78.2 years
• $50-75k: 78.4 years
• $75-100k: 72.5 years
• >$100k: 84.4 years

CONTRIBUTING FACTORS:
• Healthcare Access: 33% of disparity
• Socioeconomic Status: 22% of disparity
• Environmental Factors: 23% of disparity
• Behavioral Factors: 22% of disparity
• Biological Factors: 15% of disparity

TREND ANALYSIS:
• Disparities are widening
• Annual change in disparity: +1.6%

Social determinants explain 69% of observed mortality differences.


Instruction: Calculate Variable Universal Life life insurance premium for 68 year old male, $750,000 coverage, Standard Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $750,000
• Duration: Lifetime Coverage
• Issue Age: 68
• Sex: Male
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_68): 0.005126
• Underwriting Multiplier: 0.9x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 96% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $5767.19
• Expense Charge: $1441.80
• Reserve Accumulation: $1922.40
• Profit Margin: $480.60
• Gross Annual Premium: $9611.98

PAYMENT OPTIONS:
• Annual: $9611.98
• Semi-Annual: $4998.23 (x2 = $9996.46/year)
• Quarterly: $2547.17 (x4 = $10188.70/year)
• Monthly: $865.08 (x12 = $10380.94/year)

RESERVE CALCULATIONS:
• Net Level Premium: $7208.98
• First Year Reserve: $1922.40
• Terminal Reserve (Year -3): $290418.89

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

Internal Rate of Return: 9.7%
Profit Margin: 11.1%
Lapse Assumption: 5.8% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Variable Universal Life life insurance premium for 68 year old male, $750,000 coverage, Standard Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $750,000
• Duration: Lifetime Coverage
• Issue Age: 68
• Sex: Male
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_68): 0.005126
• Underwriting Multiplier: 0.9x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 96% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $5767.19
• Expense Charge: $1441.80
• Reserve Accumulation: $1922.40
• Profit Margin: $480.60
• Gross Annual Premium: $9611.98

PAYMENT OPTIONS:
• Annual: $9611.98
• Semi-Annual: $4998.23 (x2 = $9996.46/year)
• Quarterly: $2547.17 (x4 = $10188.70/year)
• Monthly: $865.08 (x12 = $10380.94/year)

RESERVE CALCULATIONS:
• Net Level Premium: $7208.98
• First Year Reserve: $1922.40
• Terminal Reserve (Year -3): $290418.89

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

Internal Rate of Return: 9.7%
Profit Margin: 11.1%
Lapse Assumption: 5.8% annual

Illustration assumes guaranteed rates. Actual results may vary.