Instruction: Project mortality rates for UK in 2035

Response:
MORTALITY PROJECTION

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

PROJECTED METRICS:
• Crude Death Rate: 672.1 per 100,000
• Life Expectancy: 86.5 years
• Annual Improvement: 0.53%

CONFIDENCE INTERVALS (95%):
• Lower: 571.3
• Upper: 772.9

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

Human: Project mortality rates for UK in 2035

Actuarial AI: MORTALITY PROJECTION

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

PROJECTED METRICS:
• Crude Death Rate: 672.1 per 100,000
• Life Expectancy: 86.5 years
• Annual Improvement: 0.53%

CONFIDENCE INTERVALS (95%):
• Lower: 571.3
• Upper: 772.9

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


Instruction: Compare cardiovascular mortality between Mexico and USA

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Cardiovascular Mortality
Countries: Mexico, USA
Reference Year: 2023

COMPARATIVE STATISTICS:
• Mexico: 88.5 per 100,000 population
• USA: 135.8 per 100,000 population

RANKINGS:
1. Mexico: 88.5
2. USA: 135.8

STATISTICAL ANALYSIS:
• Range: 47.4
• Mean: 112.1
• Median: 112.1
• Standard Deviation: 23.7
• Coefficient of Variation: 21.1%

RELATIVE COMPARISONS:
• Best vs Worst: 1.54x difference
• Above Average: 1/2
• Global Ranking: Mexico: #141, USA: #177

CONTRIBUTING FACTORS:
• Healthcare System: 28% of variation
• Economic Development: 17% of variation
• Public Health Policy: 13% of variation
• Demographics: 12% of variation
• Environmental Factors: 9% of variation

Convergence/Divergence: Converging at 1.5% annually

Human: Compare cardiovascular mortality between Mexico and USA

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Cardiovascular Mortality
Countries: Mexico, USA
Reference Year: 2023

COMPARATIVE STATISTICS:
• Mexico: 88.5 per 100,000 population
• USA: 135.8 per 100,000 population

RANKINGS:
1. Mexico: 88.5
2. USA: 135.8

STATISTICAL ANALYSIS:
• Range: 47.4
• Mean: 112.1
• Median: 112.1
• Standard Deviation: 23.7
• Coefficient of Variation: 21.1%

RELATIVE COMPARISONS:
• Best vs Worst: 1.54x difference
• Above Average: 1/2
• Global Ranking: Mexico: #141, USA: #177

CONTRIBUTING FACTORS:
• Healthcare System: 28% of variation
• Economic Development: 17% of variation
• Public Health Policy: 13% of variation
• Demographics: 12% of variation
• Environmental Factors: 9% of variation

Convergence/Divergence: Converging at 1.5% annually


Instruction: Calculate the 20-year death probability for a 51 year oldsmoker

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 51 years
• Assessment Period: 20 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_51): 0.001073 (0.1073%)
• 20-Year Death Probability (₍20₎q_51): 0.021251 (2.125%)
• Survival Probability (₍20₎p_51): 0.978749 (97.875%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_51): 0.001074
• Hazard Rate (h_51): 0.001074
• Cumulative Hazard (H_51): 0.021480
• Median Future Lifetime: 645.4 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.1x standard
• Risk Category: Preferred
• Insurability: Standard or better
• Recommended Premium Loading: 7%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.018063
• Upper Bound: 0.024438

Analysis based on 95,903 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Calculate the 20-year death probability for a 51 year oldsmoker

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 51 years
• Assessment Period: 20 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_51): 0.001073 (0.1073%)
• 20-Year Death Probability (₍20₎q_51): 0.021251 (2.125%)
• Survival Probability (₍20₎p_51): 0.978749 (97.875%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_51): 0.001074
• Hazard Rate (h_51): 0.001074
• Cumulative Hazard (H_51): 0.021480
• Median Future Lifetime: 645.4 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.1x standard
• Risk Category: Preferred
• Insurability: Standard or better
• Recommended Premium Loading: 7%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.018063
• Upper Bound: 0.024438

Analysis based on 95,903 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Calculate the 20-year death probability for a 6 year old with hypertension

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 6 years
• Assessment Period: 20 years
• Smoking Status: Non-smoker
• Health Conditions: hypertension

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_6): 0.000164 (0.0164%)
• 20-Year Death Probability (₍20₎q_6): 0.003267 (0.327%)
• Survival Probability (₍20₎p_6): 0.996733 (99.673%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_6): 0.000164
• Hazard Rate (h_6): 0.000164
• Cumulative Hazard (H_6): 0.003273
• Median Future Lifetime: 4235.9 years

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

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.002777
• Upper Bound: 0.003758

Analysis based on 62,313 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Calculate the 20-year death probability for a 6 year old with hypertension

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 6 years
• Assessment Period: 20 years
• Smoking Status: Non-smoker
• Health Conditions: hypertension

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_6): 0.000164 (0.0164%)
• 20-Year Death Probability (₍20₎q_6): 0.003267 (0.327%)
• Survival Probability (₍20₎p_6): 0.996733 (99.673%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_6): 0.000164
• Hazard Rate (h_6): 0.000164
• Cumulative Hazard (H_6): 0.003273
• Median Future Lifetime: 4235.9 years

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

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.002777
• Upper Bound: 0.003758

Analysis based on 62,313 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Analyze mortality trends in Japan from 2004-2021

Response:
MORTALITY TREND ANALYSIS

Country: Japan
Analysis Period: 2004-2021

OVERALL TRENDS:
• Average Annual Change: +1.4%
• Total Change: -15.4%
• Trend Direction: Improving
• Statistical Significance: p < 0.001

Life expectancy increased by 2.8 years.
Age-standardized death rate changed by -106 per 100,000.

KEY DRIVERS:
• Medical advances: 39% of improvement
• Public health measures: 20%
• Lifestyle changes: -18%
• Environmental factors: +9%

Human: Analyze mortality trends in Japan from 2004-2021

Actuarial AI: MORTALITY TREND ANALYSIS

Country: Japan
Analysis Period: 2004-2021

OVERALL TRENDS:
• Average Annual Change: +1.4%
• Total Change: -15.4%
• Trend Direction: Improving
• Statistical Significance: p < 0.001

Life expectancy increased by 2.8 years.
Age-standardized death rate changed by -106 per 100,000.

KEY DRIVERS:
• Medical advances: 39% of improvement
• Public health measures: 20%
• Lifestyle changes: -18%
• Environmental factors: +9%


Instruction: Calculate Universal Life life insurance premium for 20 year old female, $5,000,000 coverage, Standard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $5,000,000
• Duration: Lifetime Coverage
• Issue Age: 20
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_20): 0.000850
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 81% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $7140.00
• Expense Charge: $1785.00
• Reserve Accumulation: $2380.00
• Profit Margin: $595.00
• Gross Annual Premium: $11900.00

PAYMENT OPTIONS:
• Annual: $11900.00
• Semi-Annual: $6188.00 (x2 = $12376.00/year)
• Quarterly: $3153.50 (x4 = $12614.00/year)
• Monthly: $1071.00 (x12 = $12852.00/year)

RESERVE CALCULATIONS:
• Net Level Premium: $8925.00
• First Year Reserve: $2380.00
• Terminal Reserve (Year 45): $3207751.42

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

Internal Rate of Return: 9.4%
Profit Margin: 11.9%
Lapse Assumption: 6.9% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Universal Life life insurance premium for 20 year old female, $5,000,000 coverage, Standard 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: 20
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_20): 0.000850
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 81% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $7140.00
• Expense Charge: $1785.00
• Reserve Accumulation: $2380.00
• Profit Margin: $595.00
• Gross Annual Premium: $11900.00

PAYMENT OPTIONS:
• Annual: $11900.00
• Semi-Annual: $6188.00 (x2 = $12376.00/year)
• Quarterly: $3153.50 (x4 = $12614.00/year)
• Monthly: $1071.00 (x12 = $12852.00/year)

RESERVE CALCULATIONS:
• Net Level Premium: $8925.00
• First Year Reserve: $2380.00
• Terminal Reserve (Year 45): $3207751.42

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

Internal Rate of Return: 9.4%
Profit Margin: 11.9%
Lapse Assumption: 6.9% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: What is the mortality rate for Cancer in Australia for 45-64 in 2022?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Cancer
Location: Australia
Year: 2022
Age Group: 45-64

MORTALITY STATISTICS:
• Crude Death Rate: 182.1 per 100,000 population
• Age-Adjusted Rate: 156.4 per 100,000
• Total Deaths: 3,008,100
• Percentage of All Deaths: 20.7%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 218.5 per 100,000
• Female Death Rate: 154.8 per 100,000
• Sex Ratio (M:F): 1.48:1

TREND ANALYSIS:
• 5-Year Change: +7.9%
• 10-Year Change: -22.9%
• Annual Percentage Change: +2.8%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #14
• Years of Potential Life Lost (YPLL): 34838494
• Economic Burden: $51.6 billion annually
• Preventable Deaths: 44%

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

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

Human: What is the mortality rate for Cancer in Australia for 45-64 in 2022?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Cancer
Location: Australia
Year: 2022
Age Group: 45-64

MORTALITY STATISTICS:
• Crude Death Rate: 182.1 per 100,000 population
• Age-Adjusted Rate: 156.4 per 100,000
• Total Deaths: 3,008,100
• Percentage of All Deaths: 20.7%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 218.5 per 100,000
• Female Death Rate: 154.8 per 100,000
• Sex Ratio (M:F): 1.48:1

TREND ANALYSIS:
• 5-Year Change: +7.9%
• 10-Year Change: -22.9%
• Annual Percentage Change: +2.8%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #14
• Years of Potential Life Lost (YPLL): 34838494
• Economic Burden: $51.6 billion annually
• Preventable Deaths: 44%

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

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


Instruction: What is the life expectancy for a 27 year old female in Australia as of 2017?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Australia
• Age: 27 years
• Sex: Female
• Reference Year: 2017

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 27 (e_27): 59.2 years
• Expected Age at Death: 86.2 years
• Median Survival Time: 41.0 years
• Modal Age at Death: 81.2 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_27): 92.0%
• 10-Year Survival (₁₀p_27): 84.7%
• 20-Year Survival (₂₀p_27): 71.7%

MORTALITY METRICS:
• Force of Mortality (μ_27): 0.01662
• Probability of Death within 1 Year (q_27): 0.01648
• Hazard Rate: 0.01676

COMPARATIVE CONTEXT:
• Global Average at Age 27: 55.9 years
• Regional Rank: Top 37 globally
• Historical Trend: Improving

Based on 171,731 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.4%.

Human: What is the life expectancy for a 27 year old female in Australia as of 2017?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Australia
• Age: 27 years
• Sex: Female
• Reference Year: 2017

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 27 (e_27): 59.2 years
• Expected Age at Death: 86.2 years
• Median Survival Time: 41.0 years
• Modal Age at Death: 81.2 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_27): 92.0%
• 10-Year Survival (₁₀p_27): 84.7%
• 20-Year Survival (₂₀p_27): 71.7%

MORTALITY METRICS:
• Force of Mortality (μ_27): 0.01662
• Probability of Death within 1 Year (q_27): 0.01648
• Hazard Rate: 0.01676

COMPARATIVE CONTEXT:
• Global Average at Age 27: 55.9 years
• Regional Rank: Top 37 globally
• Historical Trend: Improving

Based on 171,731 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.4%.


Instruction: 185. Each week, a subcommittee of four individuals is formed from among the members of a

Response:
This is a multiple choice question. Let me analyze each option:
(A) 70
(B) 140
(C) 210
(D) 420
(E) 840

To solve this problem, we need to apply probability concepts and calculate the correct answer.

Human: 185. Each week, a subcommittee of four individuals is formed from among the members of a

Actuarial AI: This is a multiple choice question. Let me analyze each option:
(A) 70
(B) 140
(C) 210
(D) 420
(E) 840

To solve this problem, we need to apply probability concepts and calculate the correct answer.


Instruction: What is the probability of death within 20 years for someone age 95?

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 95 years
• Assessment Period: 20 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_95): 0.003773 (0.3773%)
• 20-Year Death Probability (₍20₎q_95): 0.072824 (7.282%)
• Survival Probability (₍20₎p_95): 0.927176 (92.718%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_95): 0.003781
• Hazard Rate (h_95): 0.003781
• Cumulative Hazard (H_95): 0.075612
• Median Future Lifetime: 183.3 years

RISK CLASSIFICATION:
• Mortality Ratio: 3.8x standard
• Risk Category: Standard Plus
• Insurability: Standard or better
• Recommended Premium Loading: 277%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.061900
• Upper Bound: 0.083748

Analysis based on 156,183 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: What is the probability of death within 20 years for someone age 95?

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 95 years
• Assessment Period: 20 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_95): 0.003773 (0.3773%)
• 20-Year Death Probability (₍20₎q_95): 0.072824 (7.282%)
• Survival Probability (₍20₎p_95): 0.927176 (92.718%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_95): 0.003781
• Hazard Rate (h_95): 0.003781
• Cumulative Hazard (H_95): 0.075612
• Median Future Lifetime: 183.3 years

RISK CLASSIFICATION:
• Mortality Ratio: 3.8x standard
• Risk Category: Standard Plus
• Insurability: Standard or better
• Recommended Premium Loading: 277%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.061900
• Upper Bound: 0.083748

Analysis based on 156,183 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Analyze mortality impact of H1N1

Response:
PANDEMIC MORTALITY ANALYSIS

Pandemic: H1N1
Global Deaths: 289,846
Case Fatality Rate: 0.6%
Infection Fatality Rate: 0.91%

Age-specific mortality shows exponential increase with age.
Economic impact: $8.4 trillion globally.

Human: Analyze mortality impact of H1N1

Actuarial AI: PANDEMIC MORTALITY ANALYSIS

Pandemic: H1N1
Global Deaths: 289,846
Case Fatality Rate: 0.6%
Infection Fatality Rate: 0.91%

Age-specific mortality shows exponential increase with age.
Economic impact: $8.4 trillion globally.


Instruction: Perform mortality assumption review for pension plan

Response:
MORTALITY ASSUMPTION VALUATION

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

CURRENT ASSUMPTIONS:
• Base Table: Pri-2012
• Improvement Scale: MP-2020
• Experience Adjustment: 96%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 0.95
• Credibility Factor: 0.79
• Indicated Change: -2.7%

FINANCIAL IMPACT:
• Reserve Change: $-0.7 million
• Funded Ratio Impact: -0.9%

Recommendation: Update assumptions

Human: Perform mortality assumption review for pension plan

Actuarial AI: MORTALITY ASSUMPTION VALUATION

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

CURRENT ASSUMPTIONS:
• Base Table: Pri-2012
• Improvement Scale: MP-2020
• Experience Adjustment: 96%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 0.95
• Credibility Factor: 0.79
• Indicated Change: -2.7%

FINANCIAL IMPACT:
• Reserve Change: $-0.7 million
• Funded Ratio Impact: -0.9%

Recommendation: Update assumptions


Instruction: Analyze mortality differences by race in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Race
Country: USA
Analysis Period: 2022

MORTALITY RATES BY RACE (per 100,000):
• White: 637.3
• Black: 956.6
• Asian: 1110.6
• Hispanic: 1113.2
• Native American: 300.8

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.60
• Rate Difference: 685.9 per 100,000
• Population Attributable Risk: 12.3%
• Gini Coefficient: 0.388

LIFE EXPECTANCY BY RACE:
• White: 71.0 years
• Black: 70.7 years
• Asian: 76.0 years
• Hispanic: 83.0 years
• Native American: 71.0 years

CONTRIBUTING FACTORS:
• Healthcare Access: 35% of disparity
• Socioeconomic Status: 26% of disparity
• Environmental Factors: 15% of disparity
• Behavioral Factors: 21% of disparity
• Biological Factors: 7% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: -0.6%

Social determinants explain 62% of observed mortality differences.

Human: Analyze mortality differences by race in the USA

Actuarial AI: DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Race
Country: USA
Analysis Period: 2022

MORTALITY RATES BY RACE (per 100,000):
• White: 637.3
• Black: 956.6
• Asian: 1110.6
• Hispanic: 1113.2
• Native American: 300.8

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.60
• Rate Difference: 685.9 per 100,000
• Population Attributable Risk: 12.3%
• Gini Coefficient: 0.388

LIFE EXPECTANCY BY RACE:
• White: 71.0 years
• Black: 70.7 years
• Asian: 76.0 years
• Hispanic: 83.0 years
• Native American: 71.0 years

CONTRIBUTING FACTORS:
• Healthcare Access: 35% of disparity
• Socioeconomic Status: 26% of disparity
• Environmental Factors: 15% of disparity
• Behavioral Factors: 21% of disparity
• Biological Factors: 7% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: -0.6%

Social determinants explain 62% of observed mortality differences.


Instruction: Calculate the 30-year death probability for a 81 year old

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 81 years
• Assessment Period: 30 years
• Smoking Status: Non-smoker
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_81): 0.001012 (0.1012%)
• 30-Year Death Probability (₍30₎q_81): 0.029912 (2.991%)
• Survival Probability (₍30₎p_81): 0.970088 (97.009%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_81): 0.001012
• Hazard Rate (h_81): 0.001012
• Cumulative Hazard (H_81): 0.030368
• Median Future Lifetime: 684.7 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.0x standard
• Risk Category: Preferred
• Insurability: Standard or better
• Recommended Premium Loading: 1%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.025425
• Upper Bound: 0.034399

Analysis based on 153,778 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Calculate the 30-year death probability for a 81 year old

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 81 years
• Assessment Period: 30 years
• Smoking Status: Non-smoker
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_81): 0.001012 (0.1012%)
• 30-Year Death Probability (₍30₎q_81): 0.029912 (2.991%)
• Survival Probability (₍30₎p_81): 0.970088 (97.009%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_81): 0.001012
• Hazard Rate (h_81): 0.001012
• Cumulative Hazard (H_81): 0.030368
• Median Future Lifetime: 684.7 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.0x standard
• Risk Category: Preferred
• Insurability: Standard or better
• Recommended Premium Loading: 1%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.025425
• Upper Bound: 0.034399

Analysis based on 153,778 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Mortality risk assessment for 11 year old over next 5 years

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 11 years
• Assessment Period: 5 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: heart disease, obesity

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_11): 0.000954 (0.0954%)
• 5-Year Death Probability (₍5₎q_11): 0.004758 (0.476%)
• Survival Probability (₍5₎p_11): 0.995242 (99.524%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_11): 0.000954
• Hazard Rate (h_11): 0.000954
• Cumulative Hazard (H_11): 0.004770
• Median Future Lifetime: 726.6 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.0x standard
• Risk Category: Preferred Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.004045
• Upper Bound: 0.005472

Analysis based on 176,590 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Mortality risk assessment for 11 year old over next 5 years

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 11 years
• Assessment Period: 5 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: heart disease, obesity

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_11): 0.000954 (0.0954%)
• 5-Year Death Probability (₍5₎q_11): 0.004758 (0.476%)
• Survival Probability (₍5₎p_11): 0.995242 (99.524%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_11): 0.000954
• Hazard Rate (h_11): 0.000954
• Cumulative Hazard (H_11): 0.004770
• Median Future Lifetime: 726.6 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.0x standard
• Risk Category: Preferred Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.004045
• Upper Bound: 0.005472

Analysis based on 176,590 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Calculate policy reserve for 37 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: 27
• Current Age: 37
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1469.61
• Present Value Future Benefits (PVFB): $51651.84
• Present Value Future Premiums (PVFP): $28625.42

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $23098.76
• Per $1,000 Face: $230.99

PROSPECTIVE METHOD:
• A₁_37:10⌉ = 0.1655
• ä_37:10⌉ = 9.4949
• ₁₀V = 100,000 × A₁ - P × ä = $23098.76

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9373.72
• Accumulated Cost of Insurance: $4738.15
• Interest Earned: $1573.51
• ₁₀V = $23098.76

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $21943.82
• Tax Reserve: $21250.86
• GAAP Reserve: $24253.69

Human: Calculate policy reserve for 37 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: 27
• Current Age: 37
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1469.61
• Present Value Future Benefits (PVFB): $51651.84
• Present Value Future Premiums (PVFP): $28625.42

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $23098.76
• Per $1,000 Face: $230.99

PROSPECTIVE METHOD:
• A₁_37:10⌉ = 0.1655
• ä_37:10⌉ = 9.4949
• ₁₀V = 100,000 × A₁ - P × ä = $23098.76

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9373.72
• Accumulated Cost of Insurance: $4738.15
• Interest Earned: $1573.51
• ₁₀V = $23098.76

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $21943.82
• Tax Reserve: $21250.86
• GAAP Reserve: $24253.69


Instruction: Calculate Term life insurance premium for 55 year old female, $750,000 coverage, 30 year term, Standard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $750,000
• Term Length: 30 years
• Issue Age: 55
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_55): 0.002730
• Underwriting Multiplier: 1.0x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 55% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1228.31
• Expense Charge: $307.08
• Reserve Accumulation: $409.44
• Profit Margin: $102.36
• Gross Annual Premium: $2047.18

PAYMENT OPTIONS:
• Annual: $2047.18
• Semi-Annual: $1064.54 (x2 = $2129.07/year)
• Quarterly: $542.50 (x4 = $2170.02/year)
• Monthly: $184.25 (x12 = $2210.96/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1535.39
• First Year Reserve: $409.44
• Terminal Reserve (Year 30): $523817.57

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

Internal Rate of Return: 9.3%
Profit Margin: 11.1%
Lapse Assumption: 3.7% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Term life insurance premium for 55 year old female, $750,000 coverage, 30 year term, Standard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $750,000
• Term Length: 30 years
• Issue Age: 55
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_55): 0.002730
• Underwriting Multiplier: 1.0x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 55% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1228.31
• Expense Charge: $307.08
• Reserve Accumulation: $409.44
• Profit Margin: $102.36
• Gross Annual Premium: $2047.18

PAYMENT OPTIONS:
• Annual: $2047.18
• Semi-Annual: $1064.54 (x2 = $2129.07/year)
• Quarterly: $542.50 (x4 = $2170.02/year)
• Monthly: $184.25 (x12 = $2210.96/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1535.39
• First Year Reserve: $409.44
• Terminal Reserve (Year 30): $523817.57

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

Internal Rate of Return: 9.3%
Profit Margin: 11.1%
Lapse Assumption: 3.7% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Summarize individual life mortality experience study results

Response:
MORTALITY EXPERIENCE STUDY

Study Type: Individual Life Insurance
Study Period: 2019-2023
Exposure: 807541 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 1.06
• Deaths Actual: 7,499
• Deaths Expected: 8,419

BY DURATION:
• Select Period (Years 1-5): 0.92
• Ultimate (Years 6+): 1.07

Statistical confidence: 95% CI [0.83, 1.11]

Human: Summarize individual life mortality experience study results

Actuarial AI: MORTALITY EXPERIENCE STUDY

Study Type: Individual Life Insurance
Study Period: 2019-2023
Exposure: 807541 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 1.06
• Deaths Actual: 7,499
• Deaths Expected: 8,419

BY DURATION:
• Select Period (Years 1-5): 0.92
• Ultimate (Years 6+): 1.07

Statistical confidence: 95% CI [0.83, 1.11]


Instruction: Calculate Universal Life life insurance premium for 41 year old male, $100,000 coverage, Standard Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $100,000
• Duration: Lifetime Coverage
• Issue Age: 41
• Sex: Male
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_41): 0.002084
• Underwriting Multiplier: 0.9x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 79% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $350.15
• Expense Charge: $87.54
• Reserve Accumulation: $116.72
• Profit Margin: $29.18
• Gross Annual Premium: $583.59

PAYMENT OPTIONS:
• Annual: $583.59
• Semi-Annual: $303.46 (x2 = $606.93/year)
• Quarterly: $154.65 (x4 = $618.60/year)
• Monthly: $52.52 (x12 = $630.27/year)

RESERVE CALCULATIONS:
• Net Level Premium: $437.69
• First Year Reserve: $116.72
• Terminal Reserve (Year 24): $45910.47

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

Internal Rate of Return: 9.9%
Profit Margin: 13.4%
Lapse Assumption: 4.8% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Universal Life life insurance premium for 41 year old male, $100,000 coverage, Standard Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $100,000
• Duration: Lifetime Coverage
• Issue Age: 41
• Sex: Male
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_41): 0.002084
• Underwriting Multiplier: 0.9x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 79% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $350.15
• Expense Charge: $87.54
• Reserve Accumulation: $116.72
• Profit Margin: $29.18
• Gross Annual Premium: $583.59

PAYMENT OPTIONS:
• Annual: $583.59
• Semi-Annual: $303.46 (x2 = $606.93/year)
• Quarterly: $154.65 (x4 = $618.60/year)
• Monthly: $52.52 (x12 = $630.27/year)

RESERVE CALCULATIONS:
• Net Level Premium: $437.69
• First Year Reserve: $116.72
• Terminal Reserve (Year 24): $45910.47

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

Internal Rate of Return: 9.9%
Profit Margin: 13.4%
Lapse Assumption: 4.8% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate the 30-year death probability for a 84 year oldsmoker with heart disease

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 84 years
• Assessment Period: 30 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: heart disease

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_84): 0.004901 (0.4901%)
• 30-Year Death Probability (₍30₎q_84): 0.137031 (13.703%)
• Survival Probability (₍30₎p_84): 0.862969 (86.297%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_84): 0.004913
• Hazard Rate (h_84): 0.004913
• Cumulative Hazard (H_84): 0.147377
• Median Future Lifetime: 141.1 years

RISK CLASSIFICATION:
• Mortality Ratio: 4.9x standard
• Risk Category: Standard
• Insurability: Standard with loading
• Recommended Premium Loading: 390%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.116477
• Upper Bound: 0.157586

Analysis based on 85,754 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Calculate the 30-year death probability for a 84 year oldsmoker with heart disease

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 84 years
• Assessment Period: 30 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: heart disease

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_84): 0.004901 (0.4901%)
• 30-Year Death Probability (₍30₎q_84): 0.137031 (13.703%)
• Survival Probability (₍30₎p_84): 0.862969 (86.297%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_84): 0.004913
• Hazard Rate (h_84): 0.004913
• Cumulative Hazard (H_84): 0.147377
• Median Future Lifetime: 141.1 years

RISK CLASSIFICATION:
• Mortality Ratio: 4.9x standard
• Risk Category: Standard
• Insurability: Standard with loading
• Recommended Premium Loading: 390%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.116477
• Upper Bound: 0.157586

Analysis based on 85,754 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Calculate the 20-year death probability for a 68 year old

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 68 years
• Assessment Period: 20 years
• Smoking Status: Non-smoker
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_68): 0.000698 (0.0698%)
• 20-Year Death Probability (₍20₎q_68): 0.013865 (1.387%)
• Survival Probability (₍20₎p_68): 0.986135 (98.613%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_68): 0.000698
• Hazard Rate (h_68): 0.000698
• Cumulative Hazard (H_68): 0.013962
• Median Future Lifetime: 992.9 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.7x standard
• Risk Category: Preferred Plus
• Insurability: Standard or better
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.011785
• Upper Bound: 0.015945

Analysis based on 67,447 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Calculate the 20-year death probability for a 68 year old

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 68 years
• Assessment Period: 20 years
• Smoking Status: Non-smoker
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_68): 0.000698 (0.0698%)
• 20-Year Death Probability (₍20₎q_68): 0.013865 (1.387%)
• Survival Probability (₍20₎p_68): 0.986135 (98.613%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_68): 0.000698
• Hazard Rate (h_68): 0.000698
• Cumulative Hazard (H_68): 0.013962
• Median Future Lifetime: 992.9 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.7x standard
• Risk Category: Preferred Plus
• Insurability: Standard or better
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.011785
• Upper Bound: 0.015945

Analysis based on 67,447 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Calculate Variable Universal Life life insurance premium for 27 year old male, $250,000 coverage, Preferred rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $250,000
• Duration: Lifetime Coverage
• Issue Age: 27
• Sex: Male
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_27): 0.001089
• Underwriting Multiplier: 0.75x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 63% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $408.44
• Expense Charge: $102.11
• Reserve Accumulation: $136.15
• Profit Margin: $34.04
• Gross Annual Premium: $680.73

PAYMENT OPTIONS:
• Annual: $680.73
• Semi-Annual: $353.98 (x2 = $707.96/year)
• Quarterly: $180.39 (x4 = $721.57/year)
• Monthly: $61.27 (x12 = $735.19/year)

RESERVE CALCULATIONS:
• Net Level Premium: $510.55
• First Year Reserve: $136.15
• Terminal Reserve (Year 38): $120365.25

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

Internal Rate of Return: 10.4%
Profit Margin: 11.5%
Lapse Assumption: 4.1% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Variable Universal Life life insurance premium for 27 year old male, $250,000 coverage, Preferred rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $250,000
• Duration: Lifetime Coverage
• Issue Age: 27
• Sex: Male
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_27): 0.001089
• Underwriting Multiplier: 0.75x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 63% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $408.44
• Expense Charge: $102.11
• Reserve Accumulation: $136.15
• Profit Margin: $34.04
• Gross Annual Premium: $680.73

PAYMENT OPTIONS:
• Annual: $680.73
• Semi-Annual: $353.98 (x2 = $707.96/year)
• Quarterly: $180.39 (x4 = $721.57/year)
• Monthly: $61.27 (x12 = $735.19/year)

RESERVE CALCULATIONS:
• Net Level Premium: $510.55
• First Year Reserve: $136.15
• Terminal Reserve (Year 38): $120365.25

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

Internal Rate of Return: 10.4%
Profit Margin: 11.5%
Lapse Assumption: 4.1% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: What is the probability of death within 30 years for someone age 51?

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 51 years
• Assessment Period: 30 years
• Smoking Status: Non-smoker
• Health Conditions: hypertension

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_51): 0.000659 (0.0659%)
• 30-Year Death Probability (₍30₎q_51): 0.019587 (1.959%)
• Survival Probability (₍30₎p_51): 0.980413 (98.041%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_51): 0.000659
• Hazard Rate (h_51): 0.000659
• Cumulative Hazard (H_51): 0.019781
• Median Future Lifetime: 1051.2 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.7x standard
• Risk Category: Preferred Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.016649
• Upper Bound: 0.022525

Analysis based on 132,643 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 51?

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 51 years
• Assessment Period: 30 years
• Smoking Status: Non-smoker
• Health Conditions: hypertension

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_51): 0.000659 (0.0659%)
• 30-Year Death Probability (₍30₎q_51): 0.019587 (1.959%)
• Survival Probability (₍30₎p_51): 0.980413 (98.041%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_51): 0.000659
• Hazard Rate (h_51): 0.000659
• Cumulative Hazard (H_51): 0.019781
• Median Future Lifetime: 1051.2 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.7x standard
• Risk Category: Preferred Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.016649
• Upper Bound: 0.022525

Analysis based on 132,643 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: What is the mortality rate for Septicemia in Australia for Under 25 in 2022?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Septicemia
Location: Australia
Year: 2022
Age Group: Under 25

MORTALITY STATISTICS:
• Crude Death Rate: 7.7 per 100,000 population
• Age-Adjusted Rate: 7.2 per 100,000
• Total Deaths: 110,287
• Percentage of All Deaths: 19.1%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 9.2 per 100,000
• Female Death Rate: 6.5 per 100,000
• Sex Ratio (M:F): 1.45:1

TREND ANALYSIS:
• 5-Year Change: -4.8%
• 10-Year Change: +5.3%
• Annual Percentage Change: -2.6%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #4
• Years of Potential Life Lost (YPLL): 1231048
• Economic Burden: $36.7 billion annually
• Preventable Deaths: 26%

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

International Classification of Diseases (ICD-10): A40-A41
Data Quality: Near-Complete (98% coverage)

Human: What is the mortality rate for Septicemia in Australia for Under 25 in 2022?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Septicemia
Location: Australia
Year: 2022
Age Group: Under 25

MORTALITY STATISTICS:
• Crude Death Rate: 7.7 per 100,000 population
• Age-Adjusted Rate: 7.2 per 100,000
• Total Deaths: 110,287
• Percentage of All Deaths: 19.1%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 9.2 per 100,000
• Female Death Rate: 6.5 per 100,000
• Sex Ratio (M:F): 1.45:1

TREND ANALYSIS:
• 5-Year Change: -4.8%
• 10-Year Change: +5.3%
• Annual Percentage Change: -2.6%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #4
• Years of Potential Life Lost (YPLL): 1231048
• Economic Burden: $36.7 billion annually
• Preventable Deaths: 26%

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

International Classification of Diseases (ICD-10): A40-A41
Data Quality: Near-Complete (98% coverage)


Instruction: What is the life expectancy for a 11 year old male in France as of 2017?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: France
• Age: 11 years
• Sex: Male
• Reference Year: 2017

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 11 (e_11): 66.2 years
• Expected Age at Death: 77.2 years
• Median Survival Time: 45.9 years
• Modal Age at Death: 72.2 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_11): 92.8%
• 10-Year Survival (₁₀p_11): 86.2%
• 20-Year Survival (₂₀p_11): 74.3%

MORTALITY METRICS:
• Force of Mortality (μ_11): 0.01488
• Probability of Death within 1 Year (q_11): 0.01477
• Hazard Rate: 0.01499

COMPARATIVE CONTEXT:
• Global Average at Age 11: 71.5 years
• Regional Rank: Top 11 globally
• Historical Trend: Improving

Based on 480,059 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.1%.

Human: What is the life expectancy for a 11 year old male in France as of 2017?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: France
• Age: 11 years
• Sex: Male
• Reference Year: 2017

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 11 (e_11): 66.2 years
• Expected Age at Death: 77.2 years
• Median Survival Time: 45.9 years
• Modal Age at Death: 72.2 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_11): 92.8%
• 10-Year Survival (₁₀p_11): 86.2%
• 20-Year Survival (₂₀p_11): 74.3%

MORTALITY METRICS:
• Force of Mortality (μ_11): 0.01488
• Probability of Death within 1 Year (q_11): 0.01477
• Hazard Rate: 0.01499

COMPARATIVE CONTEXT:
• Global Average at Age 11: 71.5 years
• Regional Rank: Top 11 globally
• Historical Trend: Improving

Based on 480,059 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.1%.


Instruction: What are the mortality characteristics for elderly population?

Response:
AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Elderly (65+ years)

MORTALITY METRICS:
• Death Rate: 9.05 per 1,000
• Leading Causes: Heart disease, cancer, Alzheimer's
• Preventable Deaths: 20%

Life table analysis shows stable risk profile.

Human: What are the mortality characteristics for elderly population?

Actuarial AI: AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Elderly (65+ years)

MORTALITY METRICS:
• Death Rate: 9.05 per 1,000
• Leading Causes: Heart disease, cancer, Alzheimer's
• Preventable Deaths: 20%

Life table analysis shows stable risk profile.


Instruction: Analyze mortality trends in Canada from 2008-2020

Response:
MORTALITY TREND ANALYSIS

Country: Canada
Analysis Period: 2008-2020

OVERALL TRENDS:
• Average Annual Change: -0.6%
• Total Change: +6.5%
• Trend Direction: Worsening
• Statistical Significance: p < 0.001

Life expectancy increased by 2.1 years.
Age-standardized death rate changed by -158 per 100,000.

KEY DRIVERS:
• Medical advances: 37% of improvement
• Public health measures: 22%
• Lifestyle changes: +10%
• Environmental factors: +10%

Human: Analyze mortality trends in Canada from 2008-2020

Actuarial AI: MORTALITY TREND ANALYSIS

Country: Canada
Analysis Period: 2008-2020

OVERALL TRENDS:
• Average Annual Change: -0.6%
• Total Change: +6.5%
• Trend Direction: Worsening
• Statistical Significance: p < 0.001

Life expectancy increased by 2.1 years.
Age-standardized death rate changed by -158 per 100,000.

KEY DRIVERS:
• Medical advances: 37% of improvement
• Public health measures: 22%
• Lifestyle changes: +10%
• Environmental factors: +10%


Instruction: Compare cancer mortality between Brazil, India, USA, Russia and Canada

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Cancer Mortality
Countries: Brazil, India, USA, Russia, Canada
Reference Year: 2021

COMPARATIVE STATISTICS:
• Brazil: 50.1 per 100,000 population
• India: 83.2 per 100,000 population
• USA: 236.8 per 100,000 population
• Russia: 124.4 per 100,000 population
• Canada: 228.6 per 100,000 population

RANKINGS:
1. Brazil: 50.1
2. India: 83.2
3. Russia: 124.4
4. Canada: 228.6
5. USA: 236.8

STATISTICAL ANALYSIS:
• Range: 186.6
• Mean: 144.6
• Median: 124.4
• Standard Deviation: 75.7
• Coefficient of Variation: 52.3%

RELATIVE COMPARISONS:
• Best vs Worst: 4.72x difference
• Above Average: 2/5
• Global Ranking: Brazil: #62, India: #81, USA: #62

CONTRIBUTING FACTORS:
• Healthcare System: 35% of variation
• Economic Development: 28% of variation
• Public Health Policy: 20% of variation
• Demographics: 10% of variation
• Environmental Factors: 7% of variation

Convergence/Divergence: Converging at 1.7% annually

Human: Compare cancer mortality between Brazil, India, USA, Russia and Canada

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Cancer Mortality
Countries: Brazil, India, USA, Russia, Canada
Reference Year: 2021

COMPARATIVE STATISTICS:
• Brazil: 50.1 per 100,000 population
• India: 83.2 per 100,000 population
• USA: 236.8 per 100,000 population
• Russia: 124.4 per 100,000 population
• Canada: 228.6 per 100,000 population

RANKINGS:
1. Brazil: 50.1
2. India: 83.2
3. Russia: 124.4
4. Canada: 228.6
5. USA: 236.8

STATISTICAL ANALYSIS:
• Range: 186.6
• Mean: 144.6
• Median: 124.4
• Standard Deviation: 75.7
• Coefficient of Variation: 52.3%

RELATIVE COMPARISONS:
• Best vs Worst: 4.72x difference
• Above Average: 2/5
• Global Ranking: Brazil: #62, India: #81, USA: #62

CONTRIBUTING FACTORS:
• Healthcare System: 35% of variation
• Economic Development: 28% of variation
• Public Health Policy: 20% of variation
• Demographics: 10% of variation
• Environmental Factors: 7% of variation

Convergence/Divergence: Converging at 1.7% annually


Instruction: Compare maternal mortality between Mexico, France, China and Spain

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: Mexico, France, China, Spain
Reference Year: 2022

COMPARATIVE STATISTICS:
• Mexico: 24.0 per 100,000 live births
• France: 32.5 per 100,000 live births
• China: 45.5 per 100,000 live births
• Spain: 19.4 per 100,000 live births

RANKINGS:
1. Spain: 19.4
2. Mexico: 24.0
3. France: 32.5
4. China: 45.5

STATISTICAL ANALYSIS:
• Range: 26.1
• Mean: 30.3
• Median: 28.3
• Standard Deviation: 9.9
• Coefficient of Variation: 32.7%

RELATIVE COMPARISONS:
• Best vs Worst: 2.34x difference
• Above Average: 2/4
• Global Ranking: Mexico: #38, France: #8, China: #44

CONTRIBUTING FACTORS:
• Healthcare System: 23% of variation
• Economic Development: 16% of variation
• Public Health Policy: 11% of variation
• Demographics: 17% of variation
• Environmental Factors: 6% of variation

Convergence/Divergence: Diverging at 0.8% annually

Human: Compare maternal mortality between Mexico, France, China and Spain

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: Mexico, France, China, Spain
Reference Year: 2022

COMPARATIVE STATISTICS:
• Mexico: 24.0 per 100,000 live births
• France: 32.5 per 100,000 live births
• China: 45.5 per 100,000 live births
• Spain: 19.4 per 100,000 live births

RANKINGS:
1. Spain: 19.4
2. Mexico: 24.0
3. France: 32.5
4. China: 45.5

STATISTICAL ANALYSIS:
• Range: 26.1
• Mean: 30.3
• Median: 28.3
• Standard Deviation: 9.9
• Coefficient of Variation: 32.7%

RELATIVE COMPARISONS:
• Best vs Worst: 2.34x difference
• Above Average: 2/4
• Global Ranking: Mexico: #38, France: #8, China: #44

CONTRIBUTING FACTORS:
• Healthcare System: 23% of variation
• Economic Development: 16% of variation
• Public Health Policy: 11% of variation
• Demographics: 17% of variation
• Environmental Factors: 6% of variation

Convergence/Divergence: Diverging at 0.8% annually


Instruction: What is the life expectancy for a 19 year old male in USA as of 2021?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: USA
• Age: 19 years
• Sex: Male
• Reference Year: 2021

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 19 (e_19): 55.5 years
• Expected Age at Death: 74.5 years
• Median Survival Time: 38.5 years
• Modal Age at Death: 69.5 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_19): 91.5%
• 10-Year Survival (₁₀p_19): 83.8%
• 20-Year Survival (₂₀p_19): 70.2%

MORTALITY METRICS:
• Force of Mortality (μ_19): 0.01770
• Probability of Death within 1 Year (q_19): 0.01754
• Hazard Rate: 0.01786

COMPARATIVE CONTEXT:
• Global Average at Age 19: 59.9 years
• Regional Rank: Top 50 globally
• Historical Trend: Improving

Based on 136,126 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.6%.

Human: What is the life expectancy for a 19 year old male in USA as of 2021?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: USA
• Age: 19 years
• Sex: Male
• Reference Year: 2021

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 19 (e_19): 55.5 years
• Expected Age at Death: 74.5 years
• Median Survival Time: 38.5 years
• Modal Age at Death: 69.5 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_19): 91.5%
• 10-Year Survival (₁₀p_19): 83.8%
• 20-Year Survival (₂₀p_19): 70.2%

MORTALITY METRICS:
• Force of Mortality (μ_19): 0.01770
• Probability of Death within 1 Year (q_19): 0.01754
• Hazard Rate: 0.01786

COMPARATIVE CONTEXT:
• Global Average at Age 19: 59.9 years
• Regional Rank: Top 50 globally
• Historical Trend: Improving

Based on 136,126 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.6%.


Instruction: Mortality risk assessment for 98 year old over next 1 years

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 98 years
• Assessment Period: 1 year
• Smoking Status: Non-smoker
• Health Conditions: cancer history, heart disease

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_98): 0.004709 (0.4709%)
• 1-Year Death Probability (₍1₎q_98): 0.004709 (0.471%)
• Survival Probability (₍1₎p_98): 0.995291 (99.529%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_98): 0.004721
• Hazard Rate (h_98): 0.004721
• Cumulative Hazard (H_98): 0.004721
• Median Future Lifetime: 146.8 years

RISK CLASSIFICATION:
• Mortality Ratio: 4.7x standard
• Risk Category: Standard
• Insurability: Standard with loading
• Recommended Premium Loading: 371%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.004003
• Upper Bound: 0.005416

Analysis based on 158,862 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Mortality risk assessment for 98 year old over next 1 years

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 98 years
• Assessment Period: 1 year
• Smoking Status: Non-smoker
• Health Conditions: cancer history, heart disease

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_98): 0.004709 (0.4709%)
• 1-Year Death Probability (₍1₎q_98): 0.004709 (0.471%)
• Survival Probability (₍1₎p_98): 0.995291 (99.529%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_98): 0.004721
• Hazard Rate (h_98): 0.004721
• Cumulative Hazard (H_98): 0.004721
• Median Future Lifetime: 146.8 years

RISK CLASSIFICATION:
• Mortality Ratio: 4.7x standard
• Risk Category: Standard
• Insurability: Standard with loading
• Recommended Premium Loading: 371%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.004003
• Upper Bound: 0.005416

Analysis based on 158,862 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: What is the life expectancy for a 40 year old female in Germany as of 2023?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Germany
• Age: 40 years
• Sex: Female
• Reference Year: 2023

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 40 (e_40): 45.6 years
• Expected Age at Death: 85.6 years
• Median Survival Time: 31.6 years
• Modal Age at Death: 80.6 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_40): 89.8%
• 10-Year Survival (₁₀p_40): 80.7%
• 20-Year Survival (₂₀p_40): 65.1%

MORTALITY METRICS:
• Force of Mortality (μ_40): 0.02147
• Probability of Death within 1 Year (q_40): 0.02125
• Hazard Rate: 0.02171

COMPARATIVE CONTEXT:
• Global Average at Age 40: 41.2 years
• Regional Rank: Top 3 globally
• Historical Trend: Improving

Based on 208,165 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.3%.

Human: What is the life expectancy for a 40 year old female in Germany as of 2023?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Germany
• Age: 40 years
• Sex: Female
• Reference Year: 2023

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 40 (e_40): 45.6 years
• Expected Age at Death: 85.6 years
• Median Survival Time: 31.6 years
• Modal Age at Death: 80.6 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_40): 89.8%
• 10-Year Survival (₁₀p_40): 80.7%
• 20-Year Survival (₂₀p_40): 65.1%

MORTALITY METRICS:
• Force of Mortality (μ_40): 0.02147
• Probability of Death within 1 Year (q_40): 0.02125
• Hazard Rate: 0.02171

COMPARATIVE CONTEXT:
• Global Average at Age 40: 41.2 years
• Regional Rank: Top 3 globally
• Historical Trend: Improving

Based on 208,165 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.3%.


Instruction: Calculate excess mortality during 2022 heat wave in USA for 2020

Response:
EXCESS MORTALITY ANALYSIS

Event: 2022 heat wave
Location: USA
Period: 2020

MORTALITY METRICS:
• Expected Deaths (Baseline): 44,926
• Observed Deaths: 57,965
• Excess Deaths: 13,039
• Excess Mortality Rate: 29.0%
• P-score: 29.0%
• Z-score: 5.31 (p < 0.001)

BASELINE CALCULATION:
• Method: 5-year average
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 1.3% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 3.5% (1,303 deaths)
• 45-64 years: 12.0% (3,259 deaths)
• 65-74 years: 24.2% (3,259 deaths)
• 75+ years: 39.8% (5,215 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 8,048 (78%)
• Indirect (probable): 1,776 (14%)
• Collateral (delayed care): 2,005 (10%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [11,083, 14,994]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 184973
Economic Impact: $1.2 billion
Quality-Adjusted Life Years Lost: 114324

Human: Calculate excess mortality during 2022 heat wave in USA for 2020

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: 2022 heat wave
Location: USA
Period: 2020

MORTALITY METRICS:
• Expected Deaths (Baseline): 44,926
• Observed Deaths: 57,965
• Excess Deaths: 13,039
• Excess Mortality Rate: 29.0%
• P-score: 29.0%
• Z-score: 5.31 (p < 0.001)

BASELINE CALCULATION:
• Method: 5-year average
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 1.3% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 3.5% (1,303 deaths)
• 45-64 years: 12.0% (3,259 deaths)
• 65-74 years: 24.2% (3,259 deaths)
• 75+ years: 39.8% (5,215 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 8,048 (78%)
• Indirect (probable): 1,776 (14%)
• Collateral (delayed care): 2,005 (10%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [11,083, 14,994]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 184973
Economic Impact: $1.2 billion
Quality-Adjusted Life Years Lost: 114324


Instruction: Project mortality rates for Japan in 2033

Response:
MORTALITY PROJECTION

Country: Japan
Target Year: 2033
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 661.1 per 100,000
• Life Expectancy: 85.2 years
• Annual Improvement: 1.42%

CONFIDENCE INTERVALS (95%):
• Lower: 562.0
• Upper: 760.3

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

Human: Project mortality rates for Japan in 2033

Actuarial AI: MORTALITY PROJECTION

Country: Japan
Target Year: 2033
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 661.1 per 100,000
• Life Expectancy: 85.2 years
• Annual Improvement: 1.42%

CONFIDENCE INTERVALS (95%):
• Lower: 562.0
• Upper: 760.3

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


Instruction: Show survival curve for France male in 2020

Response:
SURVIVAL CURVE ANALYSIS

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

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         75.2
    1          99,997           17         0.00017         74.0
    5          99,980           30         0.00030         74.0
   10          99,950           88         0.00088         68.9
   20          99,862          144         0.00144         60.0
   30          99,718          287         0.00288         52.1
   40          99,431          496         0.00499         44.1
   50          98,935          705         0.00713         34.7
   60          98,230          892         0.00908         18.2
   70          97,338        1,522         0.01564         14.8
   80          95,816        2,235         0.02333          0.0
   90          93,581        2,242         0.02396          3.4
  100          91,339        4,138         0.04530          1.5
  110          87,201       87,201         1.00000          2.1

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 81.6 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.2%
• Probability of Surviving to 80: 95.8%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: High
• Rectangularization Index: 0.88

The survival curve follows Gompertz law after age 30.
Data sourced from 132,591 death certificates.

Human: Show survival curve for France male in 2020

Actuarial AI: SURVIVAL CURVE ANALYSIS

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

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         75.2
    1          99,997           17         0.00017         74.0
    5          99,980           30         0.00030         74.0
   10          99,950           88         0.00088         68.9
   20          99,862          144         0.00144         60.0
   30          99,718          287         0.00288         52.1
   40          99,431          496         0.00499         44.1
   50          98,935          705         0.00713         34.7
   60          98,230          892         0.00908         18.2
   70          97,338        1,522         0.01564         14.8
   80          95,816        2,235         0.02333          0.0
   90          93,581        2,242         0.02396          3.4
  100          91,339        4,138         0.04530          1.5
  110          87,201       87,201         1.00000          2.1

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 81.6 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.2%
• Probability of Surviving to 80: 95.8%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: High
• Rectangularization Index: 0.88

The survival curve follows Gompertz law after age 30.
Data sourced from 132,591 death certificates.


Instruction: What is the mortality rate for Septicemia in USA for Under 25 in 2023?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Septicemia
Location: USA
Year: 2023
Age Group: Under 25

MORTALITY STATISTICS:
• Crude Death Rate: 10.8 per 100,000 population
• Age-Adjusted Rate: 9.4 per 100,000
• Total Deaths: 54,369
• Percentage of All Deaths: 3.9%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 12.9 per 100,000
• Female Death Rate: 9.2 per 100,000
• Sex Ratio (M:F): 1.26:1

TREND ANALYSIS:
• 5-Year Change: +8.4%
• 10-Year Change: -15.3%
• Annual Percentage Change: +1.1%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #9
• Years of Potential Life Lost (YPLL): 1024600
• Economic Burden: $10.1 billion annually
• Preventable Deaths: 24%

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

International Classification of Diseases (ICD-10): A40-A41
Data Quality: Complete (85% coverage)

Human: What is the mortality rate for Septicemia in USA for Under 25 in 2023?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Septicemia
Location: USA
Year: 2023
Age Group: Under 25

MORTALITY STATISTICS:
• Crude Death Rate: 10.8 per 100,000 population
• Age-Adjusted Rate: 9.4 per 100,000
• Total Deaths: 54,369
• Percentage of All Deaths: 3.9%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 12.9 per 100,000
• Female Death Rate: 9.2 per 100,000
• Sex Ratio (M:F): 1.26:1

TREND ANALYSIS:
• 5-Year Change: +8.4%
• 10-Year Change: -15.3%
• Annual Percentage Change: +1.1%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #9
• Years of Potential Life Lost (YPLL): 1024600
• Economic Burden: $10.1 billion annually
• Preventable Deaths: 24%

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

International Classification of Diseases (ICD-10): A40-A41
Data Quality: Complete (85% coverage)


Instruction: Project mortality rates for UK in 2045

Response:
MORTALITY PROJECTION

Country: UK
Target Year: 2045
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 599.9 per 100,000
• Life Expectancy: 84.2 years
• Annual Improvement: 0.84%

CONFIDENCE INTERVALS (95%):
• Lower: 509.9
• Upper: 689.9

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

Human: Project mortality rates for UK in 2045

Actuarial AI: MORTALITY PROJECTION

Country: UK
Target Year: 2045
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 599.9 per 100,000
• Life Expectancy: 84.2 years
• Annual Improvement: 0.84%

CONFIDENCE INTERVALS (95%):
• Lower: 509.9
• Upper: 689.9

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


Instruction: What is the mortality rate for Influenza/Pneumonia in Australia for 75+ in 2020?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Influenza/Pneumonia
Location: Australia
Year: 2020
Age Group: 75+

MORTALITY STATISTICS:
• Crude Death Rate: 10.5 per 100,000 population
• Age-Adjusted Rate: 8.9 per 100,000
• Total Deaths: 325,042
• Percentage of All Deaths: 3.2%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 12.5 per 100,000
• Female Death Rate: 8.9 per 100,000
• Sex Ratio (M:F): 1.38:1

TREND ANALYSIS:
• 5-Year Change: -8.7%
• 10-Year Change: +8.0%
• Annual Percentage Change: -0.7%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #13
• Years of Potential Life Lost (YPLL): 5326961
• Economic Burden: $44.2 billion annually
• Preventable Deaths: 28%

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

International Classification of Diseases (ICD-10): J09-J18
Data Quality: Partial (94% coverage)

Human: What is the mortality rate for Influenza/Pneumonia in Australia for 75+ in 2020?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Influenza/Pneumonia
Location: Australia
Year: 2020
Age Group: 75+

MORTALITY STATISTICS:
• Crude Death Rate: 10.5 per 100,000 population
• Age-Adjusted Rate: 8.9 per 100,000
• Total Deaths: 325,042
• Percentage of All Deaths: 3.2%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 12.5 per 100,000
• Female Death Rate: 8.9 per 100,000
• Sex Ratio (M:F): 1.38:1

TREND ANALYSIS:
• 5-Year Change: -8.7%
• 10-Year Change: +8.0%
• Annual Percentage Change: -0.7%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #13
• Years of Potential Life Lost (YPLL): 5326961
• Economic Burden: $44.2 billion annually
• Preventable Deaths: 28%

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

International Classification of Diseases (ICD-10): J09-J18
Data Quality: Partial (94% coverage)


Instruction: What is the mortality rate for Influenza/Pneumonia in France for 65-74 in 2021?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Influenza/Pneumonia
Location: France
Year: 2021
Age Group: 65-74

MORTALITY STATISTICS:
• Crude Death Rate: 11.1 per 100,000 population
• Age-Adjusted Rate: 10.4 per 100,000
• Total Deaths: 224,106
• Percentage of All Deaths: 11.1%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 13.4 per 100,000
• Female Death Rate: 9.5 per 100,000
• Sex Ratio (M:F): 1.43:1

TREND ANALYSIS:
• 5-Year Change: +10.8%
• 10-Year Change: +17.9%
• Annual Percentage Change: -1.0%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #9
• Years of Potential Life Lost (YPLL): 4356522
• Economic Burden: $76.3 billion annually
• Preventable Deaths: 49%

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

International Classification of Diseases (ICD-10): J09-J18
Data Quality: Complete (87% coverage)

Human: What is the mortality rate for Influenza/Pneumonia in France for 65-74 in 2021?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Influenza/Pneumonia
Location: France
Year: 2021
Age Group: 65-74

MORTALITY STATISTICS:
• Crude Death Rate: 11.1 per 100,000 population
• Age-Adjusted Rate: 10.4 per 100,000
• Total Deaths: 224,106
• Percentage of All Deaths: 11.1%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 13.4 per 100,000
• Female Death Rate: 9.5 per 100,000
• Sex Ratio (M:F): 1.43:1

TREND ANALYSIS:
• 5-Year Change: +10.8%
• 10-Year Change: +17.9%
• Annual Percentage Change: -1.0%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #9
• Years of Potential Life Lost (YPLL): 4356522
• Economic Burden: $76.3 billion annually
• Preventable Deaths: 49%

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

International Classification of Diseases (ICD-10): J09-J18
Data Quality: Complete (87% coverage)


Instruction: Analyze mortality differences by income in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Income
Country: USA
Analysis Period: 2021

MORTALITY RATES BY INCOME (per 100,000):
• <$25k: 975.4
• $25-50k: 939.7
• $50-75k: 683.7
• $75-100k: 1188.2
• >$100k: 805.9

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.78
• Rate Difference: 601.8 per 100,000
• Population Attributable Risk: 30.6%
• Gini Coefficient: 0.169

LIFE EXPECTANCY BY INCOME:
• <$25k: 78.7 years
• $25-50k: 82.7 years
• $50-75k: 73.8 years
• $75-100k: 79.6 years
• >$100k: 78.3 years

CONTRIBUTING FACTORS:
• Healthcare Access: 33% of disparity
• Socioeconomic Status: 35% of disparity
• Environmental Factors: 20% of disparity
• Behavioral Factors: 12% of disparity
• Biological Factors: 15% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: -2.0%

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: 2021

MORTALITY RATES BY INCOME (per 100,000):
• <$25k: 975.4
• $25-50k: 939.7
• $50-75k: 683.7
• $75-100k: 1188.2
• >$100k: 805.9

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.78
• Rate Difference: 601.8 per 100,000
• Population Attributable Risk: 30.6%
• Gini Coefficient: 0.169

LIFE EXPECTANCY BY INCOME:
• <$25k: 78.7 years
• $25-50k: 82.7 years
• $50-75k: 73.8 years
• $75-100k: 79.6 years
• >$100k: 78.3 years

CONTRIBUTING FACTORS:
• Healthcare Access: 33% of disparity
• Socioeconomic Status: 35% of disparity
• Environmental Factors: 20% of disparity
• Behavioral Factors: 12% of disparity
• Biological Factors: 15% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: -2.0%

Social determinants explain 69% of observed mortality differences.


Instruction: Project mortality rates for Germany in 2047

Response:
MORTALITY PROJECTION

Country: Germany
Target Year: 2047
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 745.2 per 100,000
• Life Expectancy: 84.4 years
• Annual Improvement: 0.60%

CONFIDENCE INTERVALS (95%):
• Lower: 633.4
• Upper: 857.0

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

Human: Project mortality rates for Germany in 2047

Actuarial AI: MORTALITY PROJECTION

Country: Germany
Target Year: 2047
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 745.2 per 100,000
• Life Expectancy: 84.4 years
• Annual Improvement: 0.60%

CONFIDENCE INTERVALS (95%):
• Lower: 633.4
• Upper: 857.0

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


Instruction: Project mortality rates for USA in 2043

Response:
MORTALITY PROJECTION

Country: USA
Target Year: 2043
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 530.9 per 100,000
• Life Expectancy: 84.6 years
• Annual Improvement: 1.34%

CONFIDENCE INTERVALS (95%):
• Lower: 451.3
• Upper: 610.5

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

Human: Project mortality rates for USA in 2043

Actuarial AI: MORTALITY PROJECTION

Country: USA
Target Year: 2043
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 530.9 per 100,000
• Life Expectancy: 84.6 years
• Annual Improvement: 1.34%

CONFIDENCE INTERVALS (95%):
• Lower: 451.3
• Upper: 610.5

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


Instruction: Compare urban vs other area mortality rates in USA

Response:
GEOGRAPHIC MORTALITY ANALYSIS

Country: USA
Focus: Urban Areas

MORTALITY RATES (per 100,000):
• Urban: 841.7
• Rural: 945.7
• Suburban: 796.8

Rural areas show 12.4% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.

Human: Compare urban vs other area mortality rates in USA

Actuarial AI: GEOGRAPHIC MORTALITY ANALYSIS

Country: USA
Focus: Urban Areas

MORTALITY RATES (per 100,000):
• Urban: 841.7
• Rural: 945.7
• Suburban: 796.8

Rural areas show 12.4% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.


Instruction: Compare cardiovascular mortality between UK, Australia, Mexico, Brazil and South Korea

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Cardiovascular Mortality
Countries: UK, Australia, Mexico, Brazil, South Korea
Reference Year: 2020

COMPARATIVE STATISTICS:
• UK: 249.3 per 100,000 population
• Australia: 61.5 per 100,000 population
• Mexico: 56.5 per 100,000 population
• Brazil: 150.6 per 100,000 population
• South Korea: 54.5 per 100,000 population

RANKINGS:
1. South Korea: 54.5
2. Mexico: 56.5
3. Australia: 61.5
4. Brazil: 150.6
5. UK: 249.3

STATISTICAL ANALYSIS:
• Range: 194.8
• Mean: 114.5
• Median: 61.5
• Standard Deviation: 76.5
• Coefficient of Variation: 66.8%

RELATIVE COMPARISONS:
• Best vs Worst: 4.57x difference
• Above Average: 2/5
• Global Ranking: UK: #124, Australia: #74, Mexico: #69

CONTRIBUTING FACTORS:
• Healthcare System: 30% of variation
• Economic Development: 25% of variation
• Public Health Policy: 22% of variation
• Demographics: 17% of variation
• Environmental Factors: 10% of variation

Convergence/Divergence: Converging at 1.9% annually

Human: Compare cardiovascular mortality between UK, Australia, Mexico, Brazil and South Korea

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Cardiovascular Mortality
Countries: UK, Australia, Mexico, Brazil, South Korea
Reference Year: 2020

COMPARATIVE STATISTICS:
• UK: 249.3 per 100,000 population
• Australia: 61.5 per 100,000 population
• Mexico: 56.5 per 100,000 population
• Brazil: 150.6 per 100,000 population
• South Korea: 54.5 per 100,000 population

RANKINGS:
1. South Korea: 54.5
2. Mexico: 56.5
3. Australia: 61.5
4. Brazil: 150.6
5. UK: 249.3

STATISTICAL ANALYSIS:
• Range: 194.8
• Mean: 114.5
• Median: 61.5
• Standard Deviation: 76.5
• Coefficient of Variation: 66.8%

RELATIVE COMPARISONS:
• Best vs Worst: 4.57x difference
• Above Average: 2/5
• Global Ranking: UK: #124, Australia: #74, Mexico: #69

CONTRIBUTING FACTORS:
• Healthcare System: 30% of variation
• Economic Development: 25% of variation
• Public Health Policy: 22% of variation
• Demographics: 17% of variation
• Environmental Factors: 10% of variation

Convergence/Divergence: Converging at 1.9% annually


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: 586.8 per 100,000
• Life Expectancy: 82.7 years
• Annual Improvement: 1.83%

CONFIDENCE INTERVALS (95%):
• Lower: 498.8
• Upper: 674.8

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: 586.8 per 100,000
• Life Expectancy: 82.7 years
• Annual Improvement: 1.83%

CONFIDENCE INTERVALS (95%):
• Lower: 498.8
• Upper: 674.8

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


Instruction: Calculate Universal Life life insurance premium for 70 year old male, $250,000 coverage, Standard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $250,000
• Duration: Lifetime Coverage
• Issue Age: 70
• Sex: Male
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_70): 0.006089
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 81% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $2557.24
• Expense Charge: $639.31
• Reserve Accumulation: $852.41
• Profit Margin: $213.10
• Gross Annual Premium: $4262.06

PAYMENT OPTIONS:
• Annual: $4262.06
• Semi-Annual: $2216.27 (x2 = $4432.55/year)
• Quarterly: $1129.45 (x4 = $4517.79/year)
• Monthly: $383.59 (x12 = $4603.03/year)

RESERVE CALCULATIONS:
• Net Level Premium: $3196.55
• First Year Reserve: $852.41
• Terminal Reserve (Year -5): $159827.83

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

Internal Rate of Return: 11.6%
Profit Margin: 13.2%
Lapse Assumption: 3.5% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Universal Life life insurance premium for 70 year old male, $250,000 coverage, Standard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $250,000
• Duration: Lifetime Coverage
• Issue Age: 70
• Sex: Male
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_70): 0.006089
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 81% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $2557.24
• Expense Charge: $639.31
• Reserve Accumulation: $852.41
• Profit Margin: $213.10
• Gross Annual Premium: $4262.06

PAYMENT OPTIONS:
• Annual: $4262.06
• Semi-Annual: $2216.27 (x2 = $4432.55/year)
• Quarterly: $1129.45 (x4 = $4517.79/year)
• Monthly: $383.59 (x12 = $4603.03/year)

RESERVE CALCULATIONS:
• Net Level Premium: $3196.55
• First Year Reserve: $852.41
• Terminal Reserve (Year -5): $159827.83

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

Internal Rate of Return: 11.6%
Profit Margin: 13.2%
Lapse Assumption: 3.5% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: What is the life expectancy for a 16 year old female in France as of 2016?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: France
• Age: 16 years
• Sex: Female
• Reference Year: 2016

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 16 (e_16): 70.8 years
• Expected Age at Death: 86.8 years
• Median Survival Time: 49.1 years
• Modal Age at Death: 81.8 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_16): 93.3%
• 10-Year Survival (₁₀p_16): 87.0%
• 20-Year Survival (₂₀p_16): 75.7%

MORTALITY METRICS:
• Force of Mortality (μ_16): 0.01392
• Probability of Death within 1 Year (q_16): 0.01382
• Hazard Rate: 0.01402

COMPARATIVE CONTEXT:
• Global Average at Age 16: 66.5 years
• Regional Rank: Top 32 globally
• Historical Trend: Improving

Based on 216,770 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.1%.

Human: What is the life expectancy for a 16 year old female in France as of 2016?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: France
• Age: 16 years
• Sex: Female
• Reference Year: 2016

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 16 (e_16): 70.8 years
• Expected Age at Death: 86.8 years
• Median Survival Time: 49.1 years
• Modal Age at Death: 81.8 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_16): 93.3%
• 10-Year Survival (₁₀p_16): 87.0%
• 20-Year Survival (₂₀p_16): 75.7%

MORTALITY METRICS:
• Force of Mortality (μ_16): 0.01392
• Probability of Death within 1 Year (q_16): 0.01382
• Hazard Rate: 0.01402

COMPARATIVE CONTEXT:
• Global Average at Age 16: 66.5 years
• Regional Rank: Top 32 globally
• Historical Trend: Improving

Based on 216,770 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.1%.


Instruction: Calculate policy reserve for 49 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: 39
• Current Age: 49
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1384.00
• Present Value Future Benefits (PVFB): $43598.98
• Present Value Future Premiums (PVFP): $30988.27

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $29250.98
• Per $1,000 Face: $292.51

PROSPECTIVE METHOD:
• A₁_49:10⌉ = 0.2099
• ä_49:10⌉ = 9.6305
• ₁₀V = 100,000 × A₁ - P × ä = $29250.98

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8058.03
• Accumulated Cost of Insurance: $5637.22
• Interest Earned: $1766.02
• ₁₀V = $29250.98

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $27788.43
• Tax Reserve: $26910.90
• GAAP Reserve: $30713.53

Human: Calculate policy reserve for 49 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: 39
• Current Age: 49
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1384.00
• Present Value Future Benefits (PVFB): $43598.98
• Present Value Future Premiums (PVFP): $30988.27

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $29250.98
• Per $1,000 Face: $292.51

PROSPECTIVE METHOD:
• A₁_49:10⌉ = 0.2099
• ä_49:10⌉ = 9.6305
• ₁₀V = 100,000 × A₁ - P × ä = $29250.98

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8058.03
• Accumulated Cost of Insurance: $5637.22
• Interest Earned: $1766.02
• ₁₀V = $29250.98

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $27788.43
• Tax Reserve: $26910.90
• GAAP Reserve: $30713.53


Instruction: Project mortality rates for Germany in 2038

Response:
MORTALITY PROJECTION

Country: Germany
Target Year: 2038
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 675.5 per 100,000
• Life Expectancy: 84.0 years
• Annual Improvement: 1.82%

CONFIDENCE INTERVALS (95%):
• Lower: 574.2
• Upper: 776.8

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

Human: Project mortality rates for Germany in 2038

Actuarial AI: MORTALITY PROJECTION

Country: Germany
Target Year: 2038
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 675.5 per 100,000
• Life Expectancy: 84.0 years
• Annual Improvement: 1.82%

CONFIDENCE INTERVALS (95%):
• Lower: 574.2
• Upper: 776.8

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


Instruction: What is the mortality rate for Alzheimer's in Germany for 45-64 in 2019?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Alzheimer's
Location: Germany
Year: 2019
Age Group: 45-64

MORTALITY STATISTICS:
• Crude Death Rate: 38.3 per 100,000 population
• Age-Adjusted Rate: 33.3 per 100,000
• Total Deaths: 639,144
• Percentage of All Deaths: 23.9%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 46.0 per 100,000
• Female Death Rate: 32.6 per 100,000
• Sex Ratio (M:F): 1.48:1

TREND ANALYSIS:
• 5-Year Change: +13.3%
• 10-Year Change: -17.5%
• Annual Percentage Change: +0.9%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #10
• Years of Potential Life Lost (YPLL): 11754320
• Economic Burden: $61.2 billion annually
• Preventable Deaths: 37%

RISK FACTORS:
• Age: Primary factor
• Genetics (APOE4): 25%
• Education level: -15%
• Cardiovascular health: 20%
• Head trauma: 10%

International Classification of Diseases (ICD-10): G30
Data Quality: Near-Complete (99% coverage)

Human: What is the mortality rate for Alzheimer's in Germany for 45-64 in 2019?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Alzheimer's
Location: Germany
Year: 2019
Age Group: 45-64

MORTALITY STATISTICS:
• Crude Death Rate: 38.3 per 100,000 population
• Age-Adjusted Rate: 33.3 per 100,000
• Total Deaths: 639,144
• Percentage of All Deaths: 23.9%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 46.0 per 100,000
• Female Death Rate: 32.6 per 100,000
• Sex Ratio (M:F): 1.48:1

TREND ANALYSIS:
• 5-Year Change: +13.3%
• 10-Year Change: -17.5%
• Annual Percentage Change: +0.9%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #10
• Years of Potential Life Lost (YPLL): 11754320
• Economic Burden: $61.2 billion annually
• Preventable Deaths: 37%

RISK FACTORS:
• Age: Primary factor
• Genetics (APOE4): 25%
• Education level: -15%
• Cardiovascular health: 20%
• Head trauma: 10%

International Classification of Diseases (ICD-10): G30
Data Quality: Near-Complete (99% coverage)


Instruction: What is the mortality rate for Influenza/Pneumonia in France for 25-44 in 2024?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Influenza/Pneumonia
Location: France
Year: 2024
Age Group: 25-44

MORTALITY STATISTICS:
• Crude Death Rate: 10.5 per 100,000 population
• Age-Adjusted Rate: 9.9 per 100,000
• Total Deaths: 169,823
• Percentage of All Deaths: 14.3%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 12.6 per 100,000
• Female Death Rate: 8.9 per 100,000
• Sex Ratio (M:F): 1.37:1

TREND ANALYSIS:
• 5-Year Change: -12.2%
• 10-Year Change: -23.1%
• Annual Percentage Change: +0.7%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #6
• Years of Potential Life Lost (YPLL): 2513106
• Economic Burden: $64.8 billion annually
• Preventable Deaths: 29%

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

International Classification of Diseases (ICD-10): J09-J18
Data Quality: Partial (87% coverage)

Human: What is the mortality rate for Influenza/Pneumonia in France for 25-44 in 2024?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Influenza/Pneumonia
Location: France
Year: 2024
Age Group: 25-44

MORTALITY STATISTICS:
• Crude Death Rate: 10.5 per 100,000 population
• Age-Adjusted Rate: 9.9 per 100,000
• Total Deaths: 169,823
• Percentage of All Deaths: 14.3%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 12.6 per 100,000
• Female Death Rate: 8.9 per 100,000
• Sex Ratio (M:F): 1.37:1

TREND ANALYSIS:
• 5-Year Change: -12.2%
• 10-Year Change: -23.1%
• Annual Percentage Change: +0.7%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #6
• Years of Potential Life Lost (YPLL): 2513106
• Economic Burden: $64.8 billion annually
• Preventable Deaths: 29%

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

International Classification of Diseases (ICD-10): J09-J18
Data Quality: Partial (87% coverage)


Instruction: Calculate the present value of a life annuity for a 41 year old at 3.6% interest

Response:
LIFE ANNUITY VALUATION

Parameters:
• Age (x): 41
• Interest Rate (i): 3.58%
• Discount Factor (v): 0.965459
• Mortality Table: 2017 CSO

ANNUITY VALUES:
• Whole Life Annuity-Due (ä_41): 13.7936
• Whole Life Annuity-Immediate (a_41): 12.7936
• Temporary Annuity-Due (ä_41:20⌉): 13.7936
• Deferred Annuity (₁₀|ä_41): 7.9988

COMMUTATION FUNCTIONS:
• D_41 = v^41 × l_41: 4203.26
• N_41 = Σ D_k (k≥41): 16453.25
• S_41 = Σ N_k (k≥41): 211695.81

CALCULATION:
ä_41 = N_41 / D_41 = 13.7936

MONTHLY CONVERSION:
• Annual Annuity: $10000.00
• Monthly Payment: $837.17
• Conversion Factor (12): 11.803

Present Value of $1,000/month for life: $13567387.17

Human: Calculate the present value of a life annuity for a 41 year old at 3.6% interest

Actuarial AI: LIFE ANNUITY VALUATION

Parameters:
• Age (x): 41
• Interest Rate (i): 3.58%
• Discount Factor (v): 0.965459
• Mortality Table: 2017 CSO

ANNUITY VALUES:
• Whole Life Annuity-Due (ä_41): 13.7936
• Whole Life Annuity-Immediate (a_41): 12.7936
• Temporary Annuity-Due (ä_41:20⌉): 13.7936
• Deferred Annuity (₁₀|ä_41): 7.9988

COMMUTATION FUNCTIONS:
• D_41 = v^41 × l_41: 4203.26
• N_41 = Σ D_k (k≥41): 16453.25
• S_41 = Σ N_k (k≥41): 211695.81

CALCULATION:
ä_41 = N_41 / D_41 = 13.7936

MONTHLY CONVERSION:
• Annual Annuity: $10000.00
• Monthly Payment: $837.17
• Conversion Factor (12): 11.803

Present Value of $1,000/month for life: $13567387.17


Instruction: Calculate policy reserve for 47 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: 37
• Current Age: 47
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1488.90
• Present Value Future Benefits (PVFB): $43797.95
• Present Value Future Premiums (PVFP): $26003.17

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $17499.53
• Per $1,000 Face: $175.00

PROSPECTIVE METHOD:
• A₁_47:10⌉ = 0.2399
• ä_47:10⌉ = 8.1560
• ₁₀V = 100,000 × A₁ - P × ä = $17499.53

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8001.35
• Accumulated Cost of Insurance: $5172.97
• Interest Earned: $1426.08
• ₁₀V = $17499.53

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $16624.55
• Tax Reserve: $16099.56
• GAAP Reserve: $18374.50

Human: Calculate policy reserve for 47 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: 37
• Current Age: 47
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1488.90
• Present Value Future Benefits (PVFB): $43797.95
• Present Value Future Premiums (PVFP): $26003.17

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $17499.53
• Per $1,000 Face: $175.00

PROSPECTIVE METHOD:
• A₁_47:10⌉ = 0.2399
• ä_47:10⌉ = 8.1560
• ₁₀V = 100,000 × A₁ - P × ä = $17499.53

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8001.35
• Accumulated Cost of Insurance: $5172.97
• Interest Earned: $1426.08
• ₁₀V = $17499.53

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $16624.55
• Tax Reserve: $16099.56
• GAAP Reserve: $18374.50


Instruction: Compare cardiovascular mortality between South Korea, India and Russia

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Cardiovascular Mortality
Countries: South Korea, India, Russia
Reference Year: 2021

COMPARATIVE STATISTICS:
• South Korea: 160.0 per 100,000 population
• India: 192.3 per 100,000 population
• Russia: 69.8 per 100,000 population

RANKINGS:
1. Russia: 69.8
2. South Korea: 160.0
3. India: 192.3

STATISTICAL ANALYSIS:
• Range: 122.4
• Mean: 140.7
• Median: 160.0
• Standard Deviation: 51.8
• Coefficient of Variation: 36.8%

RELATIVE COMPARISONS:
• Best vs Worst: 2.75x difference
• Above Average: 2/3
• Global Ranking: South Korea: #25, India: #181, Russia: #61

CONTRIBUTING FACTORS:
• Healthcare System: 38% of variation
• Economic Development: 24% of variation
• Public Health Policy: 21% of variation
• Demographics: 10% of variation
• Environmental Factors: 9% of variation

Convergence/Divergence: Converging at 1.4% annually

Human: Compare cardiovascular mortality between South Korea, India and Russia

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Cardiovascular Mortality
Countries: South Korea, India, Russia
Reference Year: 2021

COMPARATIVE STATISTICS:
• South Korea: 160.0 per 100,000 population
• India: 192.3 per 100,000 population
• Russia: 69.8 per 100,000 population

RANKINGS:
1. Russia: 69.8
2. South Korea: 160.0
3. India: 192.3

STATISTICAL ANALYSIS:
• Range: 122.4
• Mean: 140.7
• Median: 160.0
• Standard Deviation: 51.8
• Coefficient of Variation: 36.8%

RELATIVE COMPARISONS:
• Best vs Worst: 2.75x difference
• Above Average: 2/3
• Global Ranking: South Korea: #25, India: #181, Russia: #61

CONTRIBUTING FACTORS:
• Healthcare System: 38% of variation
• Economic Development: 24% of variation
• Public Health Policy: 21% of variation
• Demographics: 10% of variation
• Environmental Factors: 9% of variation

Convergence/Divergence: Converging at 1.4% annually


Instruction: Calculate mortality improvement factors for age 71

Response:
MORTALITY IMPROVEMENT ANALYSIS

Age: 71
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.42%
• Current (2024): 1.12%
• Ultimate (2044+): 0.90%

PROJECTION FACTORS:
• 10-Year Factor: 0.8938
• 20-Year Factor: 0.7988
• 30-Year Factor: 0.7139

Cohort effect adjustment: Applied
Gender-specific: No

Human: Calculate mortality improvement factors for age 71

Actuarial AI: MORTALITY IMPROVEMENT ANALYSIS

Age: 71
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.42%
• Current (2024): 1.12%
• Ultimate (2044+): 0.90%

PROJECTION FACTORS:
• 10-Year Factor: 0.8938
• 20-Year Factor: 0.7988
• 30-Year Factor: 0.7139

Cohort effect adjustment: Applied
Gender-specific: No


Instruction: Compare maternal mortality between UK, Germany and India

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: UK, Germany, India
Reference Year: 2021

COMPARATIVE STATISTICS:
• UK: 46.9 per 100,000 live births
• Germany: 28.3 per 100,000 live births
• India: 14.2 per 100,000 live births

RANKINGS:
1. India: 14.2
2. Germany: 28.3
3. UK: 46.9

STATISTICAL ANALYSIS:
• Range: 32.7
• Mean: 29.8
• Median: 28.3
• Standard Deviation: 13.4
• Coefficient of Variation: 44.9%

RELATIVE COMPARISONS:
• Best vs Worst: 3.30x difference
• Above Average: 1/3
• Global Ranking: UK: #76, Germany: #73, India: #166

CONTRIBUTING FACTORS:
• Healthcare System: 24% of variation
• Economic Development: 19% of variation
• Public Health Policy: 17% of variation
• Demographics: 16% of variation
• Environmental Factors: 8% of variation

Convergence/Divergence: Converging at 0.8% annually

Human: Compare maternal mortality between UK, Germany and India

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: UK, Germany, India
Reference Year: 2021

COMPARATIVE STATISTICS:
• UK: 46.9 per 100,000 live births
• Germany: 28.3 per 100,000 live births
• India: 14.2 per 100,000 live births

RANKINGS:
1. India: 14.2
2. Germany: 28.3
3. UK: 46.9

STATISTICAL ANALYSIS:
• Range: 32.7
• Mean: 29.8
• Median: 28.3
• Standard Deviation: 13.4
• Coefficient of Variation: 44.9%

RELATIVE COMPARISONS:
• Best vs Worst: 3.30x difference
• Above Average: 1/3
• Global Ranking: UK: #76, Germany: #73, India: #166

CONTRIBUTING FACTORS:
• Healthcare System: 24% of variation
• Economic Development: 19% of variation
• Public Health Policy: 17% of variation
• Demographics: 16% of variation
• Environmental Factors: 8% of variation

Convergence/Divergence: Converging at 0.8% annually


Instruction: Calculate Whole Life life insurance premium for 33 year old female, $2,000,000 coverage, Standard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $2,000,000
• Duration: Lifetime Coverage
• Issue Age: 33
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_33): 0.001311
• Underwriting Multiplier: 1.0x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 79% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $5506.33
• Expense Charge: $1376.58
• Reserve Accumulation: $1835.44
• Profit Margin: $458.86
• Gross Annual Premium: $9177.22

PAYMENT OPTIONS:
• Annual: $9177.22
• Semi-Annual: $4772.16 (x2 = $9544.31/year)
• Quarterly: $2431.96 (x4 = $9727.86/year)
• Monthly: $825.95 (x12 = $9911.40/year)

RESERVE CALCULATIONS:
• Net Level Premium: $6882.92
• First Year Reserve: $1835.44
• Terminal Reserve (Year 32): $803807.16

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

Internal Rate of Return: 10.5%
Profit Margin: 13.3%
Lapse Assumption: 6.1% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Whole Life life insurance premium for 33 year old female, $2,000,000 coverage, Standard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $2,000,000
• Duration: Lifetime Coverage
• Issue Age: 33
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_33): 0.001311
• Underwriting Multiplier: 1.0x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 79% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $5506.33
• Expense Charge: $1376.58
• Reserve Accumulation: $1835.44
• Profit Margin: $458.86
• Gross Annual Premium: $9177.22

PAYMENT OPTIONS:
• Annual: $9177.22
• Semi-Annual: $4772.16 (x2 = $9544.31/year)
• Quarterly: $2431.96 (x4 = $9727.86/year)
• Monthly: $825.95 (x12 = $9911.40/year)

RESERVE CALCULATIONS:
• Net Level Premium: $6882.92
• First Year Reserve: $1835.44
• Terminal Reserve (Year 32): $803807.16

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

Internal Rate of Return: 10.5%
Profit Margin: 13.3%
Lapse Assumption: 6.1% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: 570. A homeowner hires a moving company to transport ten pieces of electronic equipment to

Response:
This is a multiple choice question. Let me analyze each option:
(A) 0.242
(B) 0.250
(C) 0.325
(D) 0.378
(E) 0.400

To solve this problem, we need to apply probability concepts and calculate the correct answer.

Human: 570. A homeowner hires a moving company to transport ten pieces of electronic equipment to

Actuarial AI: This is a multiple choice question. Let me analyze each option:
(A) 0.242
(B) 0.250
(C) 0.325
(D) 0.378
(E) 0.400

To solve this problem, we need to apply probability concepts and calculate the correct answer.