Instruction: Calculate policy reserve for 58 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: 48
• Current Age: 58
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $502.70
• Present Value Future Benefits (PVFB): $42156.43
• Present Value Future Premiums (PVFP): $23140.59

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $16065.78
• Per $1,000 Face: $160.66

PROSPECTIVE METHOD:
• A₁_58:10⌉ = 0.2369
• ä_58:10⌉ = 8.3992
• ₁₀V = 100,000 × A₁ - P × ä = $16065.78

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10086.76
• Accumulated Cost of Insurance: $5324.23
• Interest Earned: $1237.66
• ₁₀V = $16065.78

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $15262.49
• Tax Reserve: $14780.52
• GAAP Reserve: $16869.07

Human: Calculate policy reserve for 58 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: 48
• Current Age: 58
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $502.70
• Present Value Future Benefits (PVFB): $42156.43
• Present Value Future Premiums (PVFP): $23140.59

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $16065.78
• Per $1,000 Face: $160.66

PROSPECTIVE METHOD:
• A₁_58:10⌉ = 0.2369
• ä_58:10⌉ = 8.3992
• ₁₀V = 100,000 × A₁ - P × ä = $16065.78

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10086.76
• Accumulated Cost of Insurance: $5324.23
• Interest Earned: $1237.66
• ₁₀V = $16065.78

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $15262.49
• Tax Reserve: $14780.52
• GAAP Reserve: $16869.07


Instruction: What is the probability of death within 30 years for someone age 35?

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 35 years
• Assessment Period: 30 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_35): 0.000680 (0.0680%)
• 30-Year Death Probability (₍30₎q_35): 0.020187 (2.019%)
• Survival Probability (₍30₎p_35): 0.979813 (97.981%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_35): 0.000680
• Hazard Rate (h_35): 0.000680
• Cumulative Hazard (H_35): 0.020394
• Median Future Lifetime: 1019.6 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: 0.017159
• Upper Bound: 0.023216

Analysis based on 140,967 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 35?

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 35 years
• Assessment Period: 30 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_35): 0.000680 (0.0680%)
• 30-Year Death Probability (₍30₎q_35): 0.020187 (2.019%)
• Survival Probability (₍30₎p_35): 0.979813 (97.981%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_35): 0.000680
• Hazard Rate (h_35): 0.000680
• Cumulative Hazard (H_35): 0.020394
• Median Future Lifetime: 1019.6 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: 0.017159
• Upper Bound: 0.023216

Analysis based on 140,967 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Calculate excess mortality during opioid crisis in India for 2020

Response:
EXCESS MORTALITY ANALYSIS

Event: opioid crisis
Location: India
Period: 2020

MORTALITY METRICS:
• Expected Deaths (Baseline): 46,033
• Observed Deaths: 53,553
• Excess Deaths: 7,520
• Excess Mortality Rate: 16.3%
• P-score: 16.3%
• Z-score: 2.46 (p < 0.001)

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

AGE-SPECIFIC EXCESS:
• 0-44 years: -1.1% (752 deaths)
• 45-64 years: 17.7% (1,880 deaths)
• 65-74 years: 17.6% (1,880 deaths)
• 75+ years: 38.7% (3,008 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 4,818 (79%)
• Indirect (probable): 1,673 (12%)
• Collateral (delayed care): 1,250 (15%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [6,392, 8,648]
• Probability of chance: < 0.001
• Power: 0.97

Years of Life Lost: 97390
Economic Impact: $1.0 billion
Quality-Adjusted Life Years Lost: 72615

Human: Calculate excess mortality during opioid crisis in India for 2020

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: opioid crisis
Location: India
Period: 2020

MORTALITY METRICS:
• Expected Deaths (Baseline): 46,033
• Observed Deaths: 53,553
• Excess Deaths: 7,520
• Excess Mortality Rate: 16.3%
• P-score: 16.3%
• Z-score: 2.46 (p < 0.001)

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

AGE-SPECIFIC EXCESS:
• 0-44 years: -1.1% (752 deaths)
• 45-64 years: 17.7% (1,880 deaths)
• 65-74 years: 17.6% (1,880 deaths)
• 75+ years: 38.7% (3,008 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 4,818 (79%)
• Indirect (probable): 1,673 (12%)
• Collateral (delayed care): 1,250 (15%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [6,392, 8,648]
• Probability of chance: < 0.001
• Power: 0.97

Years of Life Lost: 97390
Economic Impact: $1.0 billion
Quality-Adjusted Life Years Lost: 72615


Instruction: Perform mortality assumption review for life insurance portfolio

Response:
MORTALITY ASSUMPTION VALUATION

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

CURRENT ASSUMPTIONS:
• Base Table: Pri-2012
• Improvement Scale: MP-2021
• Experience Adjustment: 98%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 0.93
• Credibility Factor: 0.80
• Indicated Change: +7.9%

FINANCIAL IMPACT:
• Reserve Change: $1.2 million
• Funded Ratio Impact: -1.4%

Recommendation: Update assumptions

Human: Perform mortality assumption review for life insurance portfolio

Actuarial AI: MORTALITY ASSUMPTION VALUATION

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

CURRENT ASSUMPTIONS:
• Base Table: Pri-2012
• Improvement Scale: MP-2021
• Experience Adjustment: 98%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 0.93
• Credibility Factor: 0.80
• Indicated Change: +7.9%

FINANCIAL IMPACT:
• Reserve Change: $1.2 million
• Funded Ratio Impact: -1.4%

Recommendation: Update assumptions


Instruction: Analyze mortality impact of H1N1

Response:
PANDEMIC MORTALITY ANALYSIS

Pandemic: H1N1
Global Deaths: 186,143
Case Fatality Rate: 8.0%
Infection Fatality Rate: 0.13%

Age-specific mortality shows exponential increase with age.
Economic impact: $3.6 trillion globally.

Human: Analyze mortality impact of H1N1

Actuarial AI: PANDEMIC MORTALITY ANALYSIS

Pandemic: H1N1
Global Deaths: 186,143
Case Fatality Rate: 8.0%
Infection Fatality Rate: 0.13%

Age-specific mortality shows exponential increase with age.
Economic impact: $3.6 trillion globally.


Instruction: Calculate Variable Universal Life life insurance premium for 24 year old female, $1,000,000 coverage, Standard Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $1,000,000
• Duration: Lifetime Coverage
• Issue Age: 24
• Sex: Female
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_24): 0.000874
• Underwriting Multiplier: 0.9x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 92% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1311.17
• Expense Charge: $327.79
• Reserve Accumulation: $437.06
• Profit Margin: $109.26
• Gross Annual Premium: $2185.28

PAYMENT OPTIONS:
• Annual: $2185.28
• Semi-Annual: $1136.35 (x2 = $2272.69/year)
• Quarterly: $579.10 (x4 = $2316.40/year)
• Monthly: $196.68 (x12 = $2360.10/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1638.96
• First Year Reserve: $437.06
• Terminal Reserve (Year 41): $349528.76

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

Internal Rate of Return: 10.7%
Profit Margin: 12.5%
Lapse Assumption: 7.3% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Variable Universal Life life insurance premium for 24 year old female, $1,000,000 coverage, Standard Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $1,000,000
• Duration: Lifetime Coverage
• Issue Age: 24
• Sex: Female
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_24): 0.000874
• Underwriting Multiplier: 0.9x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 92% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1311.17
• Expense Charge: $327.79
• Reserve Accumulation: $437.06
• Profit Margin: $109.26
• Gross Annual Premium: $2185.28

PAYMENT OPTIONS:
• Annual: $2185.28
• Semi-Annual: $1136.35 (x2 = $2272.69/year)
• Quarterly: $579.10 (x4 = $2316.40/year)
• Monthly: $196.68 (x12 = $2360.10/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1638.96
• First Year Reserve: $437.06
• Terminal Reserve (Year 41): $349528.76

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

Internal Rate of Return: 10.7%
Profit Margin: 12.5%
Lapse Assumption: 7.3% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Show survival curve for Germany population in 2020

Response:
SURVIVAL CURVE ANALYSIS

Population: Germany Combined
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            2         0.00002         84.1
    1          99,998           10         0.00010         81.7
    5          99,988           21         0.00021         71.9
   10          99,967           61         0.00061         70.0
   20          99,906          137         0.00137         55.0
   30          99,769          194         0.00194         52.6
   40          99,575          362         0.00364         38.5
   50          99,213          475         0.00479         35.0
   60          98,738          782         0.00792         16.7
   70          97,956          998         0.01019         14.2
   80          96,958        1,968         0.02030          0.0
   90          94,990        1,957         0.02060          3.0
  100          93,033        3,228         0.03470          3.3
  110          89,805       89,805         1.00000          3.5

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 78.5 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.7%
• Probability of Surviving to 80: 97.0%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.84

The survival curve follows Gompertz law after age 30.
Data sourced from 137,029 death certificates.

Human: Show survival curve for Germany population in 2020

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Germany Combined
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            2         0.00002         84.1
    1          99,998           10         0.00010         81.7
    5          99,988           21         0.00021         71.9
   10          99,967           61         0.00061         70.0
   20          99,906          137         0.00137         55.0
   30          99,769          194         0.00194         52.6
   40          99,575          362         0.00364         38.5
   50          99,213          475         0.00479         35.0
   60          98,738          782         0.00792         16.7
   70          97,956          998         0.01019         14.2
   80          96,958        1,968         0.02030          0.0
   90          94,990        1,957         0.02060          3.0
  100          93,033        3,228         0.03470          3.3
  110          89,805       89,805         1.00000          3.5

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 78.5 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.7%
• Probability of Surviving to 80: 97.0%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.84

The survival curve follows Gompertz law after age 30.
Data sourced from 137,029 death certificates.


Instruction: Analyze mortality trends in Canada from 2002-2022

Response:
MORTALITY TREND ANALYSIS

Country: Canada
Analysis Period: 2002-2022

OVERALL TRENDS:
• Average Annual Change: -1.2%
• Total Change: +10.9%
• Trend Direction: Improving
• Statistical Significance: p < 0.001

Life expectancy increased by 1.7 years.
Age-standardized death rate changed by +119 per 100,000.

KEY DRIVERS:
• Medical advances: 39% of improvement
• Public health measures: 20%
• Lifestyle changes: -14%
• Environmental factors: +9%

Human: Analyze mortality trends in Canada from 2002-2022

Actuarial AI: MORTALITY TREND ANALYSIS

Country: Canada
Analysis Period: 2002-2022

OVERALL TRENDS:
• Average Annual Change: -1.2%
• Total Change: +10.9%
• Trend Direction: Improving
• Statistical Significance: p < 0.001

Life expectancy increased by 1.7 years.
Age-standardized death rate changed by +119 per 100,000.

KEY DRIVERS:
• Medical advances: 39% of improvement
• Public health measures: 20%
• Lifestyle changes: -14%
• Environmental factors: +9%


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

Response:
EXCESS MORTALITY ANALYSIS

Event: 2022 heat wave
Location: USA
Period: 2022

MORTALITY METRICS:
• Expected Deaths (Baseline): 71,312
• Observed Deaths: 90,295
• Excess Deaths: 18,983
• Excess Mortality Rate: 26.6%
• P-score: 26.6%
• Z-score: 3.53 (p < 0.001)

BASELINE CALCULATION:
• Method: Farrington surveillance
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.3% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: -0.9% (1,898 deaths)
• 45-64 years: 16.4% (4,745 deaths)
• 65-74 years: 21.8% (4,745 deaths)
• 75+ years: 38.4% (7,593 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 12,330 (67%)
• Indirect (probable): 3,137 (20%)
• Collateral (delayed care): 2,174 (11%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [16,135, 21,830]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 276098
Economic Impact: $2.0 billion
Quality-Adjusted Life Years Lost: 157612

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

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: 2022 heat wave
Location: USA
Period: 2022

MORTALITY METRICS:
• Expected Deaths (Baseline): 71,312
• Observed Deaths: 90,295
• Excess Deaths: 18,983
• Excess Mortality Rate: 26.6%
• P-score: 26.6%
• Z-score: 3.53 (p < 0.001)

BASELINE CALCULATION:
• Method: Farrington surveillance
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.3% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: -0.9% (1,898 deaths)
• 45-64 years: 16.4% (4,745 deaths)
• 65-74 years: 21.8% (4,745 deaths)
• 75+ years: 38.4% (7,593 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 12,330 (67%)
• Indirect (probable): 3,137 (20%)
• Collateral (delayed care): 2,174 (11%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [16,135, 21,830]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 276098
Economic Impact: $2.0 billion
Quality-Adjusted Life Years Lost: 157612


Instruction: What are the mortality characteristics for infant population?

Response:
AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Infant (0-1 years)

MORTALITY METRICS:
• Death Rate: 41.28 per 1,000
• Leading Causes: Congenital anomalies, prematurity, SIDS
• Preventable Deaths: 33%

Life table analysis shows high early risk.

Human: What are the mortality characteristics for infant population?

Actuarial AI: AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Infant (0-1 years)

MORTALITY METRICS:
• Death Rate: 41.28 per 1,000
• Leading Causes: Congenital anomalies, prematurity, SIDS
• Preventable Deaths: 33%

Life table analysis shows high early risk.


Instruction: Calculate policy reserve for 63 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: 53
• Current Age: 63
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $527.53
• Present Value Future Benefits (PVFB): $41430.74
• Present Value Future Premiums (PVFP): $22812.61

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $22433.66
• Per $1,000 Face: $224.34

PROSPECTIVE METHOD:
• A₁_63:10⌉ = 0.2425
• ä_63:10⌉ = 9.3756
• ₁₀V = 100,000 × A₁ - P × ä = $22433.66

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10920.96
• Accumulated Cost of Insurance: $4215.60
• Interest Earned: $1888.62
• ₁₀V = $22433.66

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $21311.98
• Tax Reserve: $20638.97
• GAAP Reserve: $23555.35

Human: Calculate policy reserve for 63 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: 53
• Current Age: 63
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $527.53
• Present Value Future Benefits (PVFB): $41430.74
• Present Value Future Premiums (PVFP): $22812.61

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $22433.66
• Per $1,000 Face: $224.34

PROSPECTIVE METHOD:
• A₁_63:10⌉ = 0.2425
• ä_63:10⌉ = 9.3756
• ₁₀V = 100,000 × A₁ - P × ä = $22433.66

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10920.96
• Accumulated Cost of Insurance: $4215.60
• Interest Earned: $1888.62
• ₁₀V = $22433.66

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $21311.98
• Tax Reserve: $20638.97
• GAAP Reserve: $23555.35


Instruction: What is the mortality rate for Septicemia in Canada for 65-74 in 2024?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Septicemia
Location: Canada
Year: 2024
Age Group: 65-74

MORTALITY STATISTICS:
• Crude Death Rate: 7.3 per 100,000 population
• Age-Adjusted Rate: 6.5 per 100,000
• Total Deaths: 233,419
• Percentage of All Deaths: 15.1%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 8.7 per 100,000
• Female Death Rate: 6.2 per 100,000
• Sex Ratio (M:F): 1.43:1

TREND ANALYSIS:
• 5-Year Change: -14.6%
• 10-Year Change: +17.8%
• Annual Percentage Change: -1.7%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #10
• Years of Potential Life Lost (YPLL): 6146955
• Economic Burden: $37.1 billion annually
• Preventable Deaths: 32%

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

International Classification of Diseases (ICD-10): A40-A41
Data Quality: Near-Complete (92% coverage)

Human: What is the mortality rate for Septicemia in Canada for 65-74 in 2024?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Septicemia
Location: Canada
Year: 2024
Age Group: 65-74

MORTALITY STATISTICS:
• Crude Death Rate: 7.3 per 100,000 population
• Age-Adjusted Rate: 6.5 per 100,000
• Total Deaths: 233,419
• Percentage of All Deaths: 15.1%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 8.7 per 100,000
• Female Death Rate: 6.2 per 100,000
• Sex Ratio (M:F): 1.43:1

TREND ANALYSIS:
• 5-Year Change: -14.6%
• 10-Year Change: +17.8%
• Annual Percentage Change: -1.7%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #10
• Years of Potential Life Lost (YPLL): 6146955
• Economic Burden: $37.1 billion annually
• Preventable Deaths: 32%

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

International Classification of Diseases (ICD-10): A40-A41
Data Quality: Near-Complete (92% coverage)


Instruction: Calculate Term life insurance premium for 34 year old female, $100,000 coverage, 30 year term, Standard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $100,000
• Term Length: 30 years
• Issue Age: 34
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_34): 0.001355
• Underwriting Multiplier: 1.0x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 54% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $81.33
• Expense Charge: $20.33
• Reserve Accumulation: $27.11
• Profit Margin: $6.78
• Gross Annual Premium: $135.55

PAYMENT OPTIONS:
• Annual: $135.55
• Semi-Annual: $70.48 (x2 = $140.97/year)
• Quarterly: $35.92 (x4 = $143.68/year)
• Monthly: $12.20 (x12 = $146.39/year)

RESERVE CALCULATIONS:
• Net Level Premium: $101.66
• First Year Reserve: $27.11
• Terminal Reserve (Year 30): $46719.07

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

Internal Rate of Return: 8.9%
Profit Margin: 11.6%
Lapse Assumption: 8.0% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Term life insurance premium for 34 year old female, $100,000 coverage, 30 year term, Standard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $100,000
• Term Length: 30 years
• Issue Age: 34
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_34): 0.001355
• Underwriting Multiplier: 1.0x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 54% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $81.33
• Expense Charge: $20.33
• Reserve Accumulation: $27.11
• Profit Margin: $6.78
• Gross Annual Premium: $135.55

PAYMENT OPTIONS:
• Annual: $135.55
• Semi-Annual: $70.48 (x2 = $140.97/year)
• Quarterly: $35.92 (x4 = $143.68/year)
• Monthly: $12.20 (x12 = $146.39/year)

RESERVE CALCULATIONS:
• Net Level Premium: $101.66
• First Year Reserve: $27.11
• Terminal Reserve (Year 30): $46719.07

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

Internal Rate of Return: 8.9%
Profit Margin: 11.6%
Lapse Assumption: 8.0% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: What are the mortality characteristics for adolescent population?

Response:
AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Adolescent (13-19 years)

MORTALITY METRICS:
• Death Rate: 18.07 per 1,000
• Leading Causes: Accidents, suicide, homicide
• Preventable Deaths: 42%

Life table analysis shows stable risk profile.

Human: What are the mortality characteristics for adolescent population?

Actuarial AI: AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Adolescent (13-19 years)

MORTALITY METRICS:
• Death Rate: 18.07 per 1,000
• Leading Causes: Accidents, suicide, homicide
• Preventable Deaths: 42%

Life table analysis shows stable risk profile.


Instruction: Calculate mortality improvement factors for age 72

Response:
MORTALITY IMPROVEMENT ANALYSIS

Age: 72
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.82%
• Current (2024): 2.21%
• Ultimate (2044+): 0.56%

PROJECTION FACTORS:
• 10-Year Factor: 0.8001
• 20-Year Factor: 0.6402
• 30-Year Factor: 0.5122

Cohort effect adjustment: Applied
Gender-specific: Yes

Human: Calculate mortality improvement factors for age 72

Actuarial AI: MORTALITY IMPROVEMENT ANALYSIS

Age: 72
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.82%
• Current (2024): 2.21%
• Ultimate (2044+): 0.56%

PROJECTION FACTORS:
• 10-Year Factor: 0.8001
• 20-Year Factor: 0.6402
• 30-Year Factor: 0.5122

Cohort effect adjustment: Applied
Gender-specific: Yes


Instruction: Calculate excess mortality during COVID-19 pandemic in Italy for Q1 2021

Response:
EXCESS MORTALITY ANALYSIS

Event: COVID-19 pandemic
Location: Italy
Period: Q1 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 31,925
• Observed Deaths: 33,696
• Excess Deaths: 1,771
• Excess Mortality Rate: 5.5%
• P-score: 5.5%
• Z-score: 3.16 (p < 0.001)

BASELINE CALCULATION:
• Method: Farrington surveillance
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 1.8% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 5.5% (177 deaths)
• 45-64 years: 16.1% (442 deaths)
• 65-74 years: 25.9% (442 deaths)
• 75+ years: 31.2% (708 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 1,180 (54%)
• Indirect (probable): 433 (12%)
• Collateral (delayed care): 228 (13%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [1,505, 2,036]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 23801
Economic Impact: $1.5 billion
Quality-Adjusted Life Years Lost: 14172

Human: Calculate excess mortality during COVID-19 pandemic in Italy for Q1 2021

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: COVID-19 pandemic
Location: Italy
Period: Q1 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 31,925
• Observed Deaths: 33,696
• Excess Deaths: 1,771
• Excess Mortality Rate: 5.5%
• P-score: 5.5%
• Z-score: 3.16 (p < 0.001)

BASELINE CALCULATION:
• Method: Farrington surveillance
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 1.8% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 5.5% (177 deaths)
• 45-64 years: 16.1% (442 deaths)
• 65-74 years: 25.9% (442 deaths)
• 75+ years: 31.2% (708 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 1,180 (54%)
• Indirect (probable): 433 (12%)
• Collateral (delayed care): 228 (13%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [1,505, 2,036]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 23801
Economic Impact: $1.5 billion
Quality-Adjusted Life Years Lost: 14172


Instruction: Calculate the 30-year death probability for a 48 year oldsmoker with obesity

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 48 years
• Assessment Period: 30 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: obesity

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_48): 0.001830 (0.1830%)
• 30-Year Death Probability (₍30₎q_48): 0.053476 (5.348%)
• Survival Probability (₍30₎p_48): 0.946524 (94.652%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_48): 0.001832
• Hazard Rate (h_48): 0.001832
• Cumulative Hazard (H_48): 0.054959
• Median Future Lifetime: 378.4 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.8x standard
• Risk Category: Preferred
• Insurability: Standard with loading
• Recommended Premium Loading: 83%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.045454
• Upper Bound: 0.061497

Analysis based on 128,219 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Calculate the 30-year death probability for a 48 year oldsmoker with obesity

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 48 years
• Assessment Period: 30 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: obesity

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_48): 0.001830 (0.1830%)
• 30-Year Death Probability (₍30₎q_48): 0.053476 (5.348%)
• Survival Probability (₍30₎p_48): 0.946524 (94.652%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_48): 0.001832
• Hazard Rate (h_48): 0.001832
• Cumulative Hazard (H_48): 0.054959
• Median Future Lifetime: 378.4 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.8x standard
• Risk Category: Preferred
• Insurability: Standard with loading
• Recommended Premium Loading: 83%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.045454
• Upper Bound: 0.061497

Analysis based on 128,219 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Show survival curve for China female in 2019

Response:
SURVIVAL CURVE ANALYSIS

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

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         79.9
    1          99,998           10         0.00010         74.3
    5          99,988           26         0.00026         75.5
   10          99,962           58         0.00058         65.8
   20          99,904           89         0.00089         56.5
   30          99,815          170         0.00170         54.4
   40          99,645          268         0.00269         43.4
   50          99,377          494         0.00497         31.8
   60          98,883          684         0.00692         24.8
   70          98,199        1,183         0.01205          6.2
   80          97,016        1,586         0.01635          0.0
   90          95,430        1,618         0.01695          1.3
  100          93,812        2,923         0.03116          4.5
  110          90,889       90,889         1.00000          1.5

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 83.3 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.0%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.89

The survival curve follows Gompertz law after age 30.
Data sourced from 351,632 death certificates.

Human: Show survival curve for China female in 2019

Actuarial AI: SURVIVAL CURVE ANALYSIS

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

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         79.9
    1          99,998           10         0.00010         74.3
    5          99,988           26         0.00026         75.5
   10          99,962           58         0.00058         65.8
   20          99,904           89         0.00089         56.5
   30          99,815          170         0.00170         54.4
   40          99,645          268         0.00269         43.4
   50          99,377          494         0.00497         31.8
   60          98,883          684         0.00692         24.8
   70          98,199        1,183         0.01205          6.2
   80          97,016        1,586         0.01635          0.0
   90          95,430        1,618         0.01695          1.3
  100          93,812        2,923         0.03116          4.5
  110          90,889       90,889         1.00000          1.5

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 83.3 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.0%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.89

The survival curve follows Gompertz law after age 30.
Data sourced from 351,632 death certificates.


Instruction: Analyze mortality trends in Germany from 2005-2021

Response:
MORTALITY TREND ANALYSIS

Country: Germany
Analysis Period: 2005-2021

OVERALL TRENDS:
• Average Annual Change: +1.5%
• Total Change: +14.3%
• Trend Direction: Improving
• Statistical Significance: p < 0.001

Life expectancy increased by 2.6 years.
Age-standardized death rate changed by -94 per 100,000.

KEY DRIVERS:
• Medical advances: 29% of improvement
• Public health measures: 23%
• Lifestyle changes: +21%
• Environmental factors: -10%

Human: Analyze mortality trends in Germany from 2005-2021

Actuarial AI: MORTALITY TREND ANALYSIS

Country: Germany
Analysis Period: 2005-2021

OVERALL TRENDS:
• Average Annual Change: +1.5%
• Total Change: +14.3%
• Trend Direction: Improving
• Statistical Significance: p < 0.001

Life expectancy increased by 2.6 years.
Age-standardized death rate changed by -94 per 100,000.

KEY DRIVERS:
• Medical advances: 29% of improvement
• Public health measures: 23%
• Lifestyle changes: +21%
• Environmental factors: -10%


Instruction: Calculate the 1-year death probability for a 98 year old with diabetes, heart disease, hypertension

Response:
MORTALITY RISK ASSESSMENT

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

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_98): 0.011170 (1.1170%)
• 1-Year Death Probability (₍1₎q_98): 0.011170 (1.117%)
• Survival Probability (₍1₎p_98): 0.988830 (98.883%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_98): 0.011233
• Hazard Rate (h_98): 0.011233
• Cumulative Hazard (H_98): 0.011233
• Median Future Lifetime: 61.7 years

RISK CLASSIFICATION:
• Mortality Ratio: 11.2x standard
• Risk Category: Substandard
• Insurability: Substandard with exclusions
• Recommended Premium Loading: 1017%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.009495
• Upper Bound: 0.012846

Analysis based on 196,405 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Calculate the 1-year death probability for a 98 year old with diabetes, heart disease, hypertension

Actuarial AI: MORTALITY RISK ASSESSMENT

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

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_98): 0.011170 (1.1170%)
• 1-Year Death Probability (₍1₎q_98): 0.011170 (1.117%)
• Survival Probability (₍1₎p_98): 0.988830 (98.883%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_98): 0.011233
• Hazard Rate (h_98): 0.011233
• Cumulative Hazard (H_98): 0.011233
• Median Future Lifetime: 61.7 years

RISK CLASSIFICATION:
• Mortality Ratio: 11.2x standard
• Risk Category: Substandard
• Insurability: Substandard with exclusions
• Recommended Premium Loading: 1017%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.009495
• Upper Bound: 0.012846

Analysis based on 196,405 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Show survival curve for India population in 2020

Response:
SURVIVAL CURVE ANALYSIS

Population: India Combined
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         77.4
    1          99,997           10         0.00010         74.2
    5          99,987           26         0.00026         75.9
   10          99,961           70         0.00070         66.1
   20          99,891          152         0.00152         61.1
   30          99,739          175         0.00175         53.2
   40          99,564          332         0.00333         43.0
   50          99,232          467         0.00471         30.7
   60          98,765          856         0.00867         17.4
   70          97,909          949         0.00969          8.8
   80          96,960        1,749         0.01804          1.1
   90          95,211        2,214         0.02325          3.6
  100          92,997        2,855         0.03070          2.3
  110          90,142       90,142         1.00000          1.2

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 81.3 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.8%
• Probability of Surviving to 80: 97.0%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 347,167 death certificates.

Human: Show survival curve for India population in 2020

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: India Combined
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         77.4
    1          99,997           10         0.00010         74.2
    5          99,987           26         0.00026         75.9
   10          99,961           70         0.00070         66.1
   20          99,891          152         0.00152         61.1
   30          99,739          175         0.00175         53.2
   40          99,564          332         0.00333         43.0
   50          99,232          467         0.00471         30.7
   60          98,765          856         0.00867         17.4
   70          97,909          949         0.00969          8.8
   80          96,960        1,749         0.01804          1.1
   90          95,211        2,214         0.02325          3.6
  100          92,997        2,855         0.03070          2.3
  110          90,142       90,142         1.00000          1.2

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 81.3 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.8%
• Probability of Surviving to 80: 97.0%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 347,167 death certificates.


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 117,382 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 117,382 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Perform mortality assumption review for pension plan

Response:
MORTALITY ASSUMPTION VALUATION

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

CURRENT ASSUMPTIONS:
• Base Table: RP-2014
• Improvement Scale: MP-2020
• Experience Adjustment: 86%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 0.90
• Credibility Factor: 0.92
• Indicated Change: +3.7%

FINANCIAL IMPACT:
• Reserve Change: $-2.4 million
• Funded Ratio Impact: -1.6%

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: RP-2014
• Improvement Scale: MP-2020
• Experience Adjustment: 86%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 0.90
• Credibility Factor: 0.92
• Indicated Change: +3.7%

FINANCIAL IMPACT:
• Reserve Change: $-2.4 million
• Funded Ratio Impact: -1.6%

Recommendation: Update assumptions


Instruction: What are the mortality characteristics for infant population?

Response:
AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Infant (0-1 years)

MORTALITY METRICS:
• Death Rate: 9.42 per 1,000
• Leading Causes: Congenital anomalies, prematurity, SIDS
• Preventable Deaths: 36%

Life table analysis shows high early risk.

Human: What are the mortality characteristics for infant population?

Actuarial AI: AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Infant (0-1 years)

MORTALITY METRICS:
• Death Rate: 9.42 per 1,000
• Leading Causes: Congenital anomalies, prematurity, SIDS
• Preventable Deaths: 36%

Life table analysis shows high early risk.


Instruction: Perform mortality assumption review for pension plan

Response:
MORTALITY ASSUMPTION VALUATION

Product: Pension Plan
Valuation Date: 12/31/2024

CURRENT ASSUMPTIONS:
• Base Table: Pri-2012
• Improvement Scale: MP-2021
• Experience Adjustment: 110%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 0.97
• Credibility Factor: 0.99
• Indicated Change: +5.2%

FINANCIAL IMPACT:
• Reserve Change: $-1.8 million
• Funded Ratio Impact: +2.0%

Recommendation: Maintain current assumptions

Human: Perform mortality assumption review for pension plan

Actuarial AI: MORTALITY ASSUMPTION VALUATION

Product: Pension Plan
Valuation Date: 12/31/2024

CURRENT ASSUMPTIONS:
• Base Table: Pri-2012
• Improvement Scale: MP-2021
• Experience Adjustment: 110%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 0.97
• Credibility Factor: 0.99
• Indicated Change: +5.2%

FINANCIAL IMPACT:
• Reserve Change: $-1.8 million
• Funded Ratio Impact: +2.0%

Recommendation: Maintain current assumptions


Instruction: What is the life expectancy for a 61 year old female in USA as of 2020?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: USA
• Age: 61 years
• Sex: Female
• Reference Year: 2020

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 61 (e_61): 25.1 years
• Expected Age at Death: 86.1 years
• Median Survival Time: 17.4 years
• Modal Age at Death: 81.1 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_61): 82.6%
• 10-Year Survival (₁₀p_61): 68.2%
• 20-Year Survival (₂₀p_61): 46.5%

MORTALITY METRICS:
• Force of Mortality (μ_61): 0.03834
• Probability of Death within 1 Year (q_61): 0.03761
• Hazard Rate: 0.03909

COMPARATIVE CONTEXT:
• Global Average at Age 61: 17.9 years
• Regional Rank: Top 9 globally
• Historical Trend: Stable

Based on 441,154 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.1%.

Human: What is the life expectancy for a 61 year old female in USA as of 2020?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: USA
• Age: 61 years
• Sex: Female
• Reference Year: 2020

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 61 (e_61): 25.1 years
• Expected Age at Death: 86.1 years
• Median Survival Time: 17.4 years
• Modal Age at Death: 81.1 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_61): 82.6%
• 10-Year Survival (₁₀p_61): 68.2%
• 20-Year Survival (₂₀p_61): 46.5%

MORTALITY METRICS:
• Force of Mortality (μ_61): 0.03834
• Probability of Death within 1 Year (q_61): 0.03761
• Hazard Rate: 0.03909

COMPARATIVE CONTEXT:
• Global Average at Age 61: 17.9 years
• Regional Rank: Top 9 globally
• Historical Trend: Stable

Based on 441,154 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.1%.


Instruction: Analyze mortality differences by race in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Race
Country: USA
Analysis Period: 2021

MORTALITY RATES BY RACE (per 100,000):
• White: 1042.3
• Black: 741.4
• Asian: 726.0
• Hispanic: 294.5
• Native American: 390.9

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.92
• Rate Difference: 557.4 per 100,000
• Population Attributable Risk: 19.9%
• Gini Coefficient: 0.394

LIFE EXPECTANCY BY RACE:
• White: 73.6 years
• Black: 82.2 years
• Asian: 74.6 years
• Hispanic: 75.6 years
• Native American: 82.9 years

CONTRIBUTING FACTORS:
• Healthcare Access: 31% of disparity
• Socioeconomic Status: 35% of disparity
• Environmental Factors: 17% of disparity
• Behavioral Factors: 22% of disparity
• Biological Factors: 9% of disparity

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

Social determinants explain 75% 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: 2021

MORTALITY RATES BY RACE (per 100,000):
• White: 1042.3
• Black: 741.4
• Asian: 726.0
• Hispanic: 294.5
• Native American: 390.9

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.92
• Rate Difference: 557.4 per 100,000
• Population Attributable Risk: 19.9%
• Gini Coefficient: 0.394

LIFE EXPECTANCY BY RACE:
• White: 73.6 years
• Black: 82.2 years
• Asian: 74.6 years
• Hispanic: 75.6 years
• Native American: 82.9 years

CONTRIBUTING FACTORS:
• Healthcare Access: 31% of disparity
• Socioeconomic Status: 35% of disparity
• Environmental Factors: 17% of disparity
• Behavioral Factors: 22% of disparity
• Biological Factors: 9% of disparity

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

Social determinants explain 75% of observed mortality differences.


Instruction: Calculate Universal Life life insurance premium for 49 year old male, $500,000 coverage, Preferred Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $500,000
• Duration: Lifetime Coverage
• Issue Age: 49
• Sex: Male
• Underwriting Class: Preferred Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_49): 0.001814
• Underwriting Multiplier: 0.6x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 65% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1523.86
• Expense Charge: $380.97
• Reserve Accumulation: $507.95
• Profit Margin: $126.99
• Gross Annual Premium: $2539.77

PAYMENT OPTIONS:
• Annual: $2539.77
• Semi-Annual: $1320.68 (x2 = $2641.37/year)
• Quarterly: $673.04 (x4 = $2692.16/year)
• Monthly: $228.58 (x12 = $2742.96/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1904.83
• First Year Reserve: $507.95
• Terminal Reserve (Year 16): $258214.45

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

Internal Rate of Return: 10.9%
Profit Margin: 10.3%
Lapse Assumption: 3.6% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Universal Life life insurance premium for 49 year old male, $500,000 coverage, Preferred Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $500,000
• Duration: Lifetime Coverage
• Issue Age: 49
• Sex: Male
• Underwriting Class: Preferred Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_49): 0.001814
• Underwriting Multiplier: 0.6x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 65% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1523.86
• Expense Charge: $380.97
• Reserve Accumulation: $507.95
• Profit Margin: $126.99
• Gross Annual Premium: $2539.77

PAYMENT OPTIONS:
• Annual: $2539.77
• Semi-Annual: $1320.68 (x2 = $2641.37/year)
• Quarterly: $673.04 (x4 = $2692.16/year)
• Monthly: $228.58 (x12 = $2742.96/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1904.83
• First Year Reserve: $507.95
• Terminal Reserve (Year 16): $258214.45

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

Internal Rate of Return: 10.9%
Profit Margin: 10.3%
Lapse Assumption: 3.6% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate the present value of a life annuity for a 40 year old at 3.5% interest

Response:
LIFE ANNUITY VALUATION

Parameters:
• Age (x): 40
• Interest Rate (i): 3.45%
• Discount Factor (v): 0.966644
• Mortality Table: 2017 CSO

ANNUITY VALUES:
• Whole Life Annuity-Due (ä_40): 13.6957
• Whole Life Annuity-Immediate (a_40): 12.6957
• Temporary Annuity-Due (ä_40:20⌉): 13.6957
• Deferred Annuity (₁₀|ä_40): 8.7034

COMMUTATION FUNCTIONS:
• D_40 = v^40 × l_40: 3862.36
• N_40 = Σ D_k (k≥40): 25351.76
• S_40 = Σ N_k (k≥40): 162342.73

CALCULATION:
ä_40 = N_40 / D_40 = 13.6957

MONTHLY CONVERSION:
• Annual Annuity: $10000.00
• Monthly Payment: $837.17
• Conversion Factor (12): 11.810

Present Value of $1,000/month for life: $13479131.48

Human: Calculate the present value of a life annuity for a 40 year old at 3.5% interest

Actuarial AI: LIFE ANNUITY VALUATION

Parameters:
• Age (x): 40
• Interest Rate (i): 3.45%
• Discount Factor (v): 0.966644
• Mortality Table: 2017 CSO

ANNUITY VALUES:
• Whole Life Annuity-Due (ä_40): 13.6957
• Whole Life Annuity-Immediate (a_40): 12.6957
• Temporary Annuity-Due (ä_40:20⌉): 13.6957
• Deferred Annuity (₁₀|ä_40): 8.7034

COMMUTATION FUNCTIONS:
• D_40 = v^40 × l_40: 3862.36
• N_40 = Σ D_k (k≥40): 25351.76
• S_40 = Σ N_k (k≥40): 162342.73

CALCULATION:
ä_40 = N_40 / D_40 = 13.6957

MONTHLY CONVERSION:
• Annual Annuity: $10000.00
• Monthly Payment: $837.17
• Conversion Factor (12): 11.810

Present Value of $1,000/month for life: $13479131.48


Instruction: What is the probability of death within 1 year for someone age 46?

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 46 years
• Assessment Period: 1 year
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_46): 0.000931 (0.0931%)
• 1-Year Death Probability (₍1₎q_46): 0.000931 (0.093%)
• Survival Probability (₍1₎p_46): 0.999069 (99.907%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_46): 0.000931
• Hazard Rate (h_46): 0.000931
• Cumulative Hazard (H_46): 0.000931
• Median Future Lifetime: 744.6 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.9x standard
• Risk Category: Preferred Plus
• Insurability: Standard or better
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.000791
• Upper Bound: 0.001070

Analysis based on 65,193 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: What is the probability of death within 1 year for someone age 46?

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 46 years
• Assessment Period: 1 year
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_46): 0.000931 (0.0931%)
• 1-Year Death Probability (₍1₎q_46): 0.000931 (0.093%)
• Survival Probability (₍1₎p_46): 0.999069 (99.907%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_46): 0.000931
• Hazard Rate (h_46): 0.000931
• Cumulative Hazard (H_46): 0.000931
• Median Future Lifetime: 744.6 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.9x standard
• Risk Category: Preferred Plus
• Insurability: Standard or better
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.000791
• Upper Bound: 0.001070

Analysis based on 65,193 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Analyze mortality trends in UK from 2006-2024

Response:
MORTALITY TREND ANALYSIS

Country: UK
Analysis Period: 2006-2024

OVERALL TRENDS:
• Average Annual Change: -1.0%
• Total Change: -9.7%
• Trend Direction: Improving
• Statistical Significance: p < 0.001

Life expectancy increased by 1.7 years.
Age-standardized death rate changed by +123 per 100,000.

KEY DRIVERS:
• Medical advances: 36% of improvement
• Public health measures: 26%
• Lifestyle changes: -16%
• Environmental factors: +12%

Human: Analyze mortality trends in UK from 2006-2024

Actuarial AI: MORTALITY TREND ANALYSIS

Country: UK
Analysis Period: 2006-2024

OVERALL TRENDS:
• Average Annual Change: -1.0%
• Total Change: -9.7%
• Trend Direction: Improving
• Statistical Significance: p < 0.001

Life expectancy increased by 1.7 years.
Age-standardized death rate changed by +123 per 100,000.

KEY DRIVERS:
• Medical advances: 36% of improvement
• Public health measures: 26%
• Lifestyle changes: -16%
• Environmental factors: +12%


Instruction: Analyze mortality differences by income in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Income
Country: USA
Analysis Period: 2019

MORTALITY RATES BY INCOME (per 100,000):
• <$25k: 852.9
• $25-50k: 730.6
• $50-75k: 539.7
• $75-100k: 589.4
• >$100k: 510.4

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.51
• Rate Difference: 559.5 per 100,000
• Population Attributable Risk: 17.7%
• Gini Coefficient: 0.365

LIFE EXPECTANCY BY INCOME:
• <$25k: 80.5 years
• $25-50k: 73.3 years
• $50-75k: 84.7 years
• $75-100k: 84.2 years
• >$100k: 77.4 years

CONTRIBUTING FACTORS:
• Healthcare Access: 38% of disparity
• Socioeconomic Status: 20% of disparity
• Environmental Factors: 24% of disparity
• Behavioral Factors: 12% of disparity
• Biological Factors: 8% of disparity

TREND ANALYSIS:
• Disparities are widening
• Annual change in disparity: +1.4%

Social determinants explain 74% of observed mortality differences.

Human: Analyze mortality differences by income in the USA

Actuarial AI: DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Income
Country: USA
Analysis Period: 2019

MORTALITY RATES BY INCOME (per 100,000):
• <$25k: 852.9
• $25-50k: 730.6
• $50-75k: 539.7
• $75-100k: 589.4
• >$100k: 510.4

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.51
• Rate Difference: 559.5 per 100,000
• Population Attributable Risk: 17.7%
• Gini Coefficient: 0.365

LIFE EXPECTANCY BY INCOME:
• <$25k: 80.5 years
• $25-50k: 73.3 years
• $50-75k: 84.7 years
• $75-100k: 84.2 years
• >$100k: 77.4 years

CONTRIBUTING FACTORS:
• Healthcare Access: 38% of disparity
• Socioeconomic Status: 20% of disparity
• Environmental Factors: 24% of disparity
• Behavioral Factors: 12% of disparity
• Biological Factors: 8% of disparity

TREND ANALYSIS:
• Disparities are widening
• Annual change in disparity: +1.4%

Social determinants explain 74% of observed mortality differences.


Instruction: Calculate policy reserve for 65 year old, 20-year term life, year 10

Response:
POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 55
• Current Age: 65
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $508.31
• Present Value Future Benefits (PVFB): $42269.62
• Present Value Future Premiums (PVFP): $33509.71

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $22395.93
• Per $1,000 Face: $223.96

PROSPECTIVE METHOD:
• A₁_65:10⌉ = 0.1973
• ä_65:10⌉ = 8.2721
• ₁₀V = 100,000 × A₁ - P × ä = $22395.93

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9452.29
• Accumulated Cost of Insurance: $3585.61
• Interest Earned: $1970.26
• ₁₀V = $22395.93

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $21276.13
• Tax Reserve: $20604.25
• GAAP Reserve: $23515.72

Human: Calculate policy reserve for 65 year old, 20-year term life, year 10

Actuarial AI: POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 55
• Current Age: 65
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $508.31
• Present Value Future Benefits (PVFB): $42269.62
• Present Value Future Premiums (PVFP): $33509.71

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $22395.93
• Per $1,000 Face: $223.96

PROSPECTIVE METHOD:
• A₁_65:10⌉ = 0.1973
• ä_65:10⌉ = 8.2721
• ₁₀V = 100,000 × A₁ - P × ä = $22395.93

RETROSPECTIVE METHOD:
• Accumulated Premiums: $9452.29
• Accumulated Cost of Insurance: $3585.61
• Interest Earned: $1970.26
• ₁₀V = $22395.93

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $21276.13
• Tax Reserve: $20604.25
• GAAP Reserve: $23515.72


Instruction: Summarize individual life mortality experience study results

Response:
MORTALITY EXPERIENCE STUDY

Study Type: Individual Life Insurance
Study Period: 2021-2022
Exposure: 138882 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 0.98
• Deaths Actual: 2,273
• Deaths Expected: 4,120

BY DURATION:
• Select Period (Years 1-5): 0.78
• Ultimate (Years 6+): 1.10

Statistical confidence: 95% CI [0.85, 1.15]

Human: Summarize individual life mortality experience study results

Actuarial AI: MORTALITY EXPERIENCE STUDY

Study Type: Individual Life Insurance
Study Period: 2021-2022
Exposure: 138882 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 0.98
• Deaths Actual: 2,273
• Deaths Expected: 4,120

BY DURATION:
• Select Period (Years 1-5): 0.78
• Ultimate (Years 6+): 1.10

Statistical confidence: 95% CI [0.85, 1.15]


Instruction: Analyze mortality impact of Spanish Flu

Response:
PANDEMIC MORTALITY ANALYSIS

Pandemic: Spanish Flu
Global Deaths: 50,951,889
Case Fatality Rate: 9.2%
Infection Fatality Rate: 0.02%

Age-specific mortality shows exponential increase with age.
Economic impact: $6.6 trillion globally.

Human: Analyze mortality impact of Spanish Flu

Actuarial AI: PANDEMIC MORTALITY ANALYSIS

Pandemic: Spanish Flu
Global Deaths: 50,951,889
Case Fatality Rate: 9.2%
Infection Fatality Rate: 0.02%

Age-specific mortality shows exponential increase with age.
Economic impact: $6.6 trillion globally.


Instruction: Compare cancer mortality between France, USA, UK, Spain and Russia

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Cancer Mortality
Countries: France, USA, UK, Spain, Russia
Reference Year: 2020

COMPARATIVE STATISTICS:
• France: 212.3 per 100,000 population
• USA: 180.8 per 100,000 population
• UK: 203.4 per 100,000 population
• Spain: 50.5 per 100,000 population
• Russia: 109.7 per 100,000 population

RANKINGS:
1. Spain: 50.5
2. Russia: 109.7
3. USA: 180.8
4. UK: 203.4
5. France: 212.3

STATISTICAL ANALYSIS:
• Range: 161.8
• Mean: 151.3
• Median: 180.8
• Standard Deviation: 62.0
• Coefficient of Variation: 40.9%

RELATIVE COMPARISONS:
• Best vs Worst: 4.20x difference
• Above Average: 3/5
• Global Ranking: France: #186, USA: #111, UK: #121

CONTRIBUTING FACTORS:
• Healthcare System: 28% of variation
• Economic Development: 29% of variation
• Public Health Policy: 15% of variation
• Demographics: 10% of variation
• Environmental Factors: 10% of variation

Convergence/Divergence: Converging at 0.8% annually

Human: Compare cancer mortality between France, USA, UK, Spain and Russia

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Cancer Mortality
Countries: France, USA, UK, Spain, Russia
Reference Year: 2020

COMPARATIVE STATISTICS:
• France: 212.3 per 100,000 population
• USA: 180.8 per 100,000 population
• UK: 203.4 per 100,000 population
• Spain: 50.5 per 100,000 population
• Russia: 109.7 per 100,000 population

RANKINGS:
1. Spain: 50.5
2. Russia: 109.7
3. USA: 180.8
4. UK: 203.4
5. France: 212.3

STATISTICAL ANALYSIS:
• Range: 161.8
• Mean: 151.3
• Median: 180.8
• Standard Deviation: 62.0
• Coefficient of Variation: 40.9%

RELATIVE COMPARISONS:
• Best vs Worst: 4.20x difference
• Above Average: 3/5
• Global Ranking: France: #186, USA: #111, UK: #121

CONTRIBUTING FACTORS:
• Healthcare System: 28% of variation
• Economic Development: 29% of variation
• Public Health Policy: 15% of variation
• Demographics: 10% of variation
• Environmental Factors: 10% of variation

Convergence/Divergence: Converging at 0.8% annually


Instruction: Summarize individual life mortality experience study results

Response:
MORTALITY EXPERIENCE STUDY

Study Type: Individual Life Insurance
Study Period: 2021-2023
Exposure: 198224 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 1.04
• Deaths Actual: 4,859
• Deaths Expected: 9,712

BY DURATION:
• Select Period (Years 1-5): 0.71
• Ultimate (Years 6+): 1.00

Statistical confidence: 95% CI [0.95, 1.10]

Human: Summarize individual life mortality experience study results

Actuarial AI: MORTALITY EXPERIENCE STUDY

Study Type: Individual Life Insurance
Study Period: 2021-2023
Exposure: 198224 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 1.04
• Deaths Actual: 4,859
• Deaths Expected: 9,712

BY DURATION:
• Select Period (Years 1-5): 0.71
• Ultimate (Years 6+): 1.00

Statistical confidence: 95% CI [0.95, 1.10]


Instruction: Perform mortality assumption review for life insurance portfolio

Response:
MORTALITY ASSUMPTION VALUATION

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

CURRENT ASSUMPTIONS:
• Base Table: Pri-2012
• Improvement Scale: MP-2019
• Experience Adjustment: 106%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 0.98
• Credibility Factor: 0.98
• Indicated Change: +4.8%

FINANCIAL IMPACT:
• Reserve Change: $8.4 million
• Funded Ratio Impact: -1.5%

Recommendation: Maintain current assumptions

Human: Perform mortality assumption review for life insurance portfolio

Actuarial AI: MORTALITY ASSUMPTION VALUATION

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

CURRENT ASSUMPTIONS:
• Base Table: Pri-2012
• Improvement Scale: MP-2019
• Experience Adjustment: 106%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 0.98
• Credibility Factor: 0.98
• Indicated Change: +4.8%

FINANCIAL IMPACT:
• Reserve Change: $8.4 million
• Funded Ratio Impact: -1.5%

Recommendation: Maintain current assumptions


Instruction: Project mortality rates for USA in 2044

Response:
MORTALITY PROJECTION

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

PROJECTED METRICS:
• Crude Death Rate: 529.3 per 100,000
• Life Expectancy: 82.7 years
• Annual Improvement: 1.18%

CONFIDENCE INTERVALS (95%):
• Lower: 449.9
• Upper: 608.7

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

Human: Project mortality rates for USA in 2044

Actuarial AI: MORTALITY PROJECTION

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

PROJECTED METRICS:
• Crude Death Rate: 529.3 per 100,000
• Life Expectancy: 82.7 years
• Annual Improvement: 1.18%

CONFIDENCE INTERVALS (95%):
• Lower: 449.9
• Upper: 608.7

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


Instruction: Calculate Universal Life life insurance premium for 58 year old male, $500,000 coverage, Preferred Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $500,000
• Duration: Lifetime Coverage
• Issue Age: 58
• Sex: Male
• Underwriting Class: Preferred Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_58): 0.002449
• Underwriting Multiplier: 0.6x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 81% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $2057.00
• Expense Charge: $514.25
• Reserve Accumulation: $685.67
• Profit Margin: $171.42
• Gross Annual Premium: $3428.34

PAYMENT OPTIONS:
• Annual: $3428.34
• Semi-Annual: $1782.74 (x2 = $3565.47/year)
• Quarterly: $908.51 (x4 = $3634.04/year)
• Monthly: $308.55 (x12 = $3702.60/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2571.25
• First Year Reserve: $685.67
• Terminal Reserve (Year 7): $243012.89

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

Internal Rate of Return: 8.5%
Profit Margin: 14.3%
Lapse Assumption: 7.2% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Universal Life life insurance premium for 58 year old male, $500,000 coverage, Preferred Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $500,000
• Duration: Lifetime Coverage
• Issue Age: 58
• Sex: Male
• Underwriting Class: Preferred Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_58): 0.002449
• Underwriting Multiplier: 0.6x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 81% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $2057.00
• Expense Charge: $514.25
• Reserve Accumulation: $685.67
• Profit Margin: $171.42
• Gross Annual Premium: $3428.34

PAYMENT OPTIONS:
• Annual: $3428.34
• Semi-Annual: $1782.74 (x2 = $3565.47/year)
• Quarterly: $908.51 (x4 = $3634.04/year)
• Monthly: $308.55 (x12 = $3702.60/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2571.25
• First Year Reserve: $685.67
• Terminal Reserve (Year 7): $243012.89

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

Internal Rate of Return: 8.5%
Profit Margin: 14.3%
Lapse Assumption: 7.2% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Analyze mortality patterns for 1951 birth cohort

Response:
BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1951
Current Age: 73 years
Cohort Size at Birth: 2,769,492

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 74.5 years
• Current Life Expectancy: 78.3 years
• Survival to Current Age: 67.1%

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

MORTALITY PATTERN:
• Peak Infant Mortality: 36.6 per 1,000
• Current Mortality Rate: 49.1 per 1,000
• Improvement Since Birth: 50%

Cohort effects explain 15% of mortality variation.

Human: Analyze mortality patterns for 1951 birth cohort

Actuarial AI: BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1951
Current Age: 73 years
Cohort Size at Birth: 2,769,492

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 74.5 years
• Current Life Expectancy: 78.3 years
• Survival to Current Age: 67.1%

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

MORTALITY PATTERN:
• Peak Infant Mortality: 36.6 per 1,000
• Current Mortality Rate: 49.1 per 1,000
• Improvement Since Birth: 50%

Cohort effects explain 15% of mortality variation.


Instruction: Calculate policy reserve for 66 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: 56
• Current Age: 66
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1452.40
• Present Value Future Benefits (PVFB): $59215.49
• Present Value Future Premiums (PVFP): $27292.14

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $25783.90
• Per $1,000 Face: $257.84

PROSPECTIVE METHOD:
• A₁_66:10⌉ = 0.2482
• ä_66:10⌉ = 8.1718
• ₁₀V = 100,000 × A₁ - P × ä = $25783.90

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10081.63
• Accumulated Cost of Insurance: $3847.17
• Interest Earned: $1569.19
• ₁₀V = $25783.90

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $24494.71
• Tax Reserve: $23721.19
• GAAP Reserve: $27073.10

Human: Calculate policy reserve for 66 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: 56
• Current Age: 66
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1452.40
• Present Value Future Benefits (PVFB): $59215.49
• Present Value Future Premiums (PVFP): $27292.14

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $25783.90
• Per $1,000 Face: $257.84

PROSPECTIVE METHOD:
• A₁_66:10⌉ = 0.2482
• ä_66:10⌉ = 8.1718
• ₁₀V = 100,000 × A₁ - P × ä = $25783.90

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10081.63
• Accumulated Cost of Insurance: $3847.17
• Interest Earned: $1569.19
• ₁₀V = $25783.90

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $24494.71
• Tax Reserve: $23721.19
• GAAP Reserve: $27073.10


Instruction: Calculate Term life insurance premium for 38 year old female, $500,000 coverage, 15 year term, Standard Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $500,000
• Term Length: 15 years
• Issue Age: 38
• Sex: Female
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_38): 0.001394
• Underwriting Multiplier: 0.9x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 86% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $418.18
• Expense Charge: $104.54
• Reserve Accumulation: $139.39
• Profit Margin: $34.85
• Gross Annual Premium: $696.96

PAYMENT OPTIONS:
• Annual: $696.96
• Semi-Annual: $362.42 (x2 = $724.84/year)
• Quarterly: $184.69 (x4 = $738.78/year)
• Monthly: $62.73 (x12 = $752.72/year)

RESERVE CALCULATIONS:
• Net Level Premium: $522.72
• First Year Reserve: $139.39
• Terminal Reserve (Year 15): $261386.76

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

Internal Rate of Return: 9.2%
Profit Margin: 10.2%
Lapse Assumption: 5.1% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Term life insurance premium for 38 year old female, $500,000 coverage, 15 year term, Standard Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $500,000
• Term Length: 15 years
• Issue Age: 38
• Sex: Female
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_38): 0.001394
• Underwriting Multiplier: 0.9x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 86% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $418.18
• Expense Charge: $104.54
• Reserve Accumulation: $139.39
• Profit Margin: $34.85
• Gross Annual Premium: $696.96

PAYMENT OPTIONS:
• Annual: $696.96
• Semi-Annual: $362.42 (x2 = $724.84/year)
• Quarterly: $184.69 (x4 = $738.78/year)
• Monthly: $62.73 (x12 = $752.72/year)

RESERVE CALCULATIONS:
• Net Level Premium: $522.72
• First Year Reserve: $139.39
• Terminal Reserve (Year 15): $261386.76

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

Internal Rate of Return: 9.2%
Profit Margin: 10.2%
Lapse Assumption: 5.1% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: What is the life expectancy for a 67 year old male in Canada as of 2018?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Canada
• Age: 67 years
• Sex: Male
• Reference Year: 2018

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 67 (e_67): 8.5 years
• Expected Age at Death: 75.5 years
• Median Survival Time: 5.9 years
• Modal Age at Death: 70.5 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_67): 59.1%
• 10-Year Survival (₁₀p_67): 34.9%
• 20-Year Survival (₂₀p_67): 12.2%

MORTALITY METRICS:
• Force of Mortality (μ_67): 0.10529
• Probability of Death within 1 Year (q_67): 0.09994
• Hazard Rate: 0.11126

COMPARATIVE CONTEXT:
• Global Average at Age 67: 15.1 years
• Regional Rank: Top 48 globally
• Historical Trend: Improving

Based on 120,781 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.4%.

Human: What is the life expectancy for a 67 year old male in Canada as of 2018?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Canada
• Age: 67 years
• Sex: Male
• Reference Year: 2018

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 67 (e_67): 8.5 years
• Expected Age at Death: 75.5 years
• Median Survival Time: 5.9 years
• Modal Age at Death: 70.5 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_67): 59.1%
• 10-Year Survival (₁₀p_67): 34.9%
• 20-Year Survival (₂₀p_67): 12.2%

MORTALITY METRICS:
• Force of Mortality (μ_67): 0.10529
• Probability of Death within 1 Year (q_67): 0.09994
• Hazard Rate: 0.11126

COMPARATIVE CONTEXT:
• Global Average at Age 67: 15.1 years
• Regional Rank: Top 48 globally
• Historical Trend: Improving

Based on 120,781 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.4%.


Instruction: Calculate Whole Life life insurance premium for 27 year old female, $750,000 coverage, Substandard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $750,000
• Duration: Lifetime Coverage
• Issue Age: 27
• Sex: Female
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_27): 0.001610
• Underwriting Multiplier: 1.5x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 96% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $2535.86
• Expense Charge: $633.97
• Reserve Accumulation: $845.29
• Profit Margin: $211.32
• Gross Annual Premium: $4226.44

PAYMENT OPTIONS:
• Annual: $4226.44
• Semi-Annual: $2197.75 (x2 = $4395.50/year)
• Quarterly: $1120.01 (x4 = $4480.03/year)
• Monthly: $380.38 (x12 = $4564.56/year)

RESERVE CALCULATIONS:
• Net Level Premium: $3169.83
• First Year Reserve: $845.29
• Terminal Reserve (Year 38): $475022.22

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

Internal Rate of Return: 11.7%
Profit Margin: 14.8%
Lapse Assumption: 6.6% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Whole Life life insurance premium for 27 year old female, $750,000 coverage, Substandard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $750,000
• Duration: Lifetime Coverage
• Issue Age: 27
• Sex: Female
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_27): 0.001610
• Underwriting Multiplier: 1.5x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 96% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $2535.86
• Expense Charge: $633.97
• Reserve Accumulation: $845.29
• Profit Margin: $211.32
• Gross Annual Premium: $4226.44

PAYMENT OPTIONS:
• Annual: $4226.44
• Semi-Annual: $2197.75 (x2 = $4395.50/year)
• Quarterly: $1120.01 (x4 = $4480.03/year)
• Monthly: $380.38 (x12 = $4564.56/year)

RESERVE CALCULATIONS:
• Net Level Premium: $3169.83
• First Year Reserve: $845.29
• Terminal Reserve (Year 38): $475022.22

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

Internal Rate of Return: 11.7%
Profit Margin: 14.8%
Lapse Assumption: 6.6% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Project mortality rates for China in 2048

Response:
MORTALITY PROJECTION

Country: China
Target Year: 2048
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 845.3 per 100,000
• Life Expectancy: 89.4 years
• Annual Improvement: 0.66%

CONFIDENCE INTERVALS (95%):
• Lower: 718.5
• Upper: 972.1

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

Human: Project mortality rates for China in 2048

Actuarial AI: MORTALITY PROJECTION

Country: China
Target Year: 2048
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 845.3 per 100,000
• Life Expectancy: 89.4 years
• Annual Improvement: 0.66%

CONFIDENCE INTERVALS (95%):
• Lower: 718.5
• Upper: 972.1

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


Instruction: Analyze mortality differences by income in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Income
Country: USA
Analysis Period: 2021

MORTALITY RATES BY INCOME (per 100,000):
• <$25k: 793.8
• $25-50k: 1044.6
• $50-75k: 957.2
• $75-100k: 860.5
• >$100k: 447.4

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.63
• Rate Difference: 600.6 per 100,000
• Population Attributable Risk: 32.6%
• Gini Coefficient: 0.257

LIFE EXPECTANCY BY INCOME:
• <$25k: 78.3 years
• $25-50k: 81.2 years
• $50-75k: 72.4 years
• $75-100k: 73.7 years
• >$100k: 78.7 years

CONTRIBUTING FACTORS:
• Healthcare Access: 30% of disparity
• Socioeconomic Status: 32% of disparity
• Environmental Factors: 17% of disparity
• Behavioral Factors: 22% of disparity
• Biological Factors: 8% of disparity

TREND ANALYSIS:
• Disparities are widening
• Annual change in disparity: -1.8%

Social determinants explain 80% 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: 793.8
• $25-50k: 1044.6
• $50-75k: 957.2
• $75-100k: 860.5
• >$100k: 447.4

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.63
• Rate Difference: 600.6 per 100,000
• Population Attributable Risk: 32.6%
• Gini Coefficient: 0.257

LIFE EXPECTANCY BY INCOME:
• <$25k: 78.3 years
• $25-50k: 81.2 years
• $50-75k: 72.4 years
• $75-100k: 73.7 years
• >$100k: 78.7 years

CONTRIBUTING FACTORS:
• Healthcare Access: 30% of disparity
• Socioeconomic Status: 32% of disparity
• Environmental Factors: 17% of disparity
• Behavioral Factors: 22% of disparity
• Biological Factors: 8% of disparity

TREND ANALYSIS:
• Disparities are widening
• Annual change in disparity: -1.8%

Social determinants explain 80% of observed mortality differences.


Instruction: Analyze mortality differences by ethnicity in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Ethnicity
Country: USA
Analysis Period: 2022

MORTALITY RATES BY ETHNICITY (per 100,000):
• Non-Hispanic White: 605.1
• Hispanic: 317.6
• Non-Hispanic Black: 556.1
• Asian/Pacific Islander: 342.5

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.28
• Rate Difference: 480.4 per 100,000
• Population Attributable Risk: 16.8%
• Gini Coefficient: 0.288

LIFE EXPECTANCY BY ETHNICITY:
• Non-Hispanic White: 76.5 years
• Hispanic: 82.4 years
• Non-Hispanic Black: 80.6 years
• Asian/Pacific Islander: 83.3 years

CONTRIBUTING FACTORS:
• Healthcare Access: 36% of disparity
• Socioeconomic Status: 30% of disparity
• Environmental Factors: 13% of disparity
• Behavioral Factors: 18% of disparity
• Biological Factors: 14% of disparity

TREND ANALYSIS:
• Disparities are widening
• Annual change in disparity: -0.9%

Social determinants explain 71% of observed mortality differences.

Human: Analyze mortality differences by ethnicity in the USA

Actuarial AI: DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Ethnicity
Country: USA
Analysis Period: 2022

MORTALITY RATES BY ETHNICITY (per 100,000):
• Non-Hispanic White: 605.1
• Hispanic: 317.6
• Non-Hispanic Black: 556.1
• Asian/Pacific Islander: 342.5

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.28
• Rate Difference: 480.4 per 100,000
• Population Attributable Risk: 16.8%
• Gini Coefficient: 0.288

LIFE EXPECTANCY BY ETHNICITY:
• Non-Hispanic White: 76.5 years
• Hispanic: 82.4 years
• Non-Hispanic Black: 80.6 years
• Asian/Pacific Islander: 83.3 years

CONTRIBUTING FACTORS:
• Healthcare Access: 36% of disparity
• Socioeconomic Status: 30% of disparity
• Environmental Factors: 13% of disparity
• Behavioral Factors: 18% of disparity
• Biological Factors: 14% of disparity

TREND ANALYSIS:
• Disparities are widening
• Annual change in disparity: -0.9%

Social determinants explain 71% of observed mortality differences.


Instruction: Calculate excess mortality during 2022 heat wave in Germany for Q4 2021

Response:
EXCESS MORTALITY ANALYSIS

Event: 2022 heat wave
Location: Germany
Period: Q4 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 54,641
• Observed Deaths: 80,237
• Excess Deaths: 25,596
• Excess Mortality Rate: 46.8%
• P-score: 46.8%
• Z-score: 4.36 (p < 0.001)

BASELINE CALCULATION:
• Method: 5-year average
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.0% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: -0.5% (2,559 deaths)
• 45-64 years: 12.4% (6,399 deaths)
• 65-74 years: 26.7% (6,399 deaths)
• 75+ years: 30.5% (10,238 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 15,203 (61%)
• Indirect (probable): 5,662 (10%)
• Collateral (delayed care): 3,732 (18%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [21,756, 29,435]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 293967
Economic Impact: $3.2 billion
Quality-Adjusted Life Years Lost: 261747

Human: Calculate excess mortality during 2022 heat wave in Germany for Q4 2021

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: 2022 heat wave
Location: Germany
Period: Q4 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 54,641
• Observed Deaths: 80,237
• Excess Deaths: 25,596
• Excess Mortality Rate: 46.8%
• P-score: 46.8%
• Z-score: 4.36 (p < 0.001)

BASELINE CALCULATION:
• Method: 5-year average
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.0% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: -0.5% (2,559 deaths)
• 45-64 years: 12.4% (6,399 deaths)
• 65-74 years: 26.7% (6,399 deaths)
• 75+ years: 30.5% (10,238 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 15,203 (61%)
• Indirect (probable): 5,662 (10%)
• Collateral (delayed care): 3,732 (18%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [21,756, 29,435]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 293967
Economic Impact: $3.2 billion
Quality-Adjusted Life Years Lost: 261747


Instruction: Show survival curve for Japan female in 2019

Response:
SURVIVAL CURVE ANALYSIS

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

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         82.6
    1          99,998            8         0.00008         80.6
    5          99,990           20         0.00020         75.4
   10          99,970           65         0.00065         72.9
   20          99,905          125         0.00125         64.6
   30          99,780          150         0.00150         47.9
   40          99,630          298         0.00299         43.9
   50          99,332          375         0.00378         27.0
   60          98,957          660         0.00667         16.5
   70          98,297        1,112         0.01131         10.6
   80          97,185        1,306         0.01344          0.0
   90          95,879        1,857         0.01937          4.7
  100          94,022        2,206         0.02346          2.1
  110          91,816       91,816         1.00000          3.7

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 77.2 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 99.0%
• Probability of Surviving to 80: 97.2%

CURVE CHARACTERISTICS:
• Type: Type I (Rectangular)
• Compression: High
• Rectangularization Index: 0.84

The survival curve follows Gompertz law after age 30.
Data sourced from 364,492 death certificates.

Human: Show survival curve for Japan female in 2019

Actuarial AI: SURVIVAL CURVE ANALYSIS

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

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         82.6
    1          99,998            8         0.00008         80.6
    5          99,990           20         0.00020         75.4
   10          99,970           65         0.00065         72.9
   20          99,905          125         0.00125         64.6
   30          99,780          150         0.00150         47.9
   40          99,630          298         0.00299         43.9
   50          99,332          375         0.00378         27.0
   60          98,957          660         0.00667         16.5
   70          98,297        1,112         0.01131         10.6
   80          97,185        1,306         0.01344          0.0
   90          95,879        1,857         0.01937          4.7
  100          94,022        2,206         0.02346          2.1
  110          91,816       91,816         1.00000          3.7

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 77.2 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 99.0%
• Probability of Surviving to 80: 97.2%

CURVE CHARACTERISTICS:
• Type: Type I (Rectangular)
• Compression: High
• Rectangularization Index: 0.84

The survival curve follows Gompertz law after age 30.
Data sourced from 364,492 death certificates.


Instruction: Summarize annuity mortality experience study results

Response:
MORTALITY EXPERIENCE STUDY

Study Type: Annuity Insurance
Study Period: 2021-2024
Exposure: 934425 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 0.91
• Deaths Actual: 1,807
• Deaths Expected: 8,250

BY DURATION:
• Select Period (Years 1-5): 0.80
• Ultimate (Years 6+): 0.96

Statistical confidence: 95% CI [0.84, 1.12]

Human: Summarize annuity mortality experience study results

Actuarial AI: MORTALITY EXPERIENCE STUDY

Study Type: Annuity Insurance
Study Period: 2021-2024
Exposure: 934425 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 0.91
• Deaths Actual: 1,807
• Deaths Expected: 8,250

BY DURATION:
• Select Period (Years 1-5): 0.80
• Ultimate (Years 6+): 0.96

Statistical confidence: 95% CI [0.84, 1.12]


Instruction: Compare cardiovascular mortality between Spain and UK

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Cardiovascular Mortality
Countries: Spain, UK
Reference Year: 2020

COMPARATIVE STATISTICS:
• Spain: 143.2 per 100,000 population
• UK: 186.6 per 100,000 population

RANKINGS:
1. Spain: 143.2
2. UK: 186.6

STATISTICAL ANALYSIS:
• Range: 43.4
• Mean: 164.9
• Median: 164.9
• Standard Deviation: 21.7
• Coefficient of Variation: 13.2%

RELATIVE COMPARISONS:
• Best vs Worst: 1.30x difference
• Above Average: 1/2
• Global Ranking: Spain: #169, UK: #166

CONTRIBUTING FACTORS:
• Healthcare System: 27% of variation
• Economic Development: 15% of variation
• Public Health Policy: 18% of variation
• Demographics: 17% of variation
• Environmental Factors: 12% of variation

Convergence/Divergence: Diverging at 0.9% annually

Human: Compare cardiovascular mortality between Spain and UK

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Cardiovascular Mortality
Countries: Spain, UK
Reference Year: 2020

COMPARATIVE STATISTICS:
• Spain: 143.2 per 100,000 population
• UK: 186.6 per 100,000 population

RANKINGS:
1. Spain: 143.2
2. UK: 186.6

STATISTICAL ANALYSIS:
• Range: 43.4
• Mean: 164.9
• Median: 164.9
• Standard Deviation: 21.7
• Coefficient of Variation: 13.2%

RELATIVE COMPARISONS:
• Best vs Worst: 1.30x difference
• Above Average: 1/2
• Global Ranking: Spain: #169, UK: #166

CONTRIBUTING FACTORS:
• Healthcare System: 27% of variation
• Economic Development: 15% of variation
• Public Health Policy: 18% of variation
• Demographics: 17% of variation
• Environmental Factors: 12% of variation

Convergence/Divergence: Diverging at 0.9% annually


Instruction: What is the mortality rate for Cancer in Germany for 65-74 in 2022?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Cancer
Location: Germany
Year: 2022
Age Group: 65-74

MORTALITY STATISTICS:
• Crude Death Rate: 168.7 per 100,000 population
• Age-Adjusted Rate: 157.2 per 100,000
• Total Deaths: 6,903,288
• Percentage of All Deaths: 23.9%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 202.4 per 100,000
• Female Death Rate: 143.4 per 100,000
• Sex Ratio (M:F): 1.23:1

TREND ANALYSIS:
• 5-Year Change: -4.5%
• 10-Year Change: +19.1%
• Annual Percentage Change: +2.3%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #1
• Years of Potential Life Lost (YPLL): 155964735
• Economic Burden: $21.1 billion annually
• Preventable Deaths: 58%

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

International Classification of Diseases (ICD-10): C00-C97
Data Quality: Partial (85% coverage)

Human: What is the mortality rate for Cancer in Germany for 65-74 in 2022?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Cancer
Location: Germany
Year: 2022
Age Group: 65-74

MORTALITY STATISTICS:
• Crude Death Rate: 168.7 per 100,000 population
• Age-Adjusted Rate: 157.2 per 100,000
• Total Deaths: 6,903,288
• Percentage of All Deaths: 23.9%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 202.4 per 100,000
• Female Death Rate: 143.4 per 100,000
• Sex Ratio (M:F): 1.23:1

TREND ANALYSIS:
• 5-Year Change: -4.5%
• 10-Year Change: +19.1%
• Annual Percentage Change: +2.3%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #1
• Years of Potential Life Lost (YPLL): 155964735
• Economic Burden: $21.1 billion annually
• Preventable Deaths: 58%

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

International Classification of Diseases (ICD-10): C00-C97
Data Quality: Partial (85% coverage)


Instruction: Compare rural vs other area mortality rates in USA

Response:
GEOGRAPHIC MORTALITY ANALYSIS

Country: USA
Focus: Rural Areas

MORTALITY RATES (per 100,000):
• Urban: 837.2
• Rural: 1052.4
• Suburban: 754.6

Rural areas show 25.7% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.

Human: Compare rural vs other area mortality rates in USA

Actuarial AI: GEOGRAPHIC MORTALITY ANALYSIS

Country: USA
Focus: Rural Areas

MORTALITY RATES (per 100,000):
• Urban: 837.2
• Rural: 1052.4
• Suburban: 754.6

Rural areas show 25.7% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.


Instruction: Calculate Whole Life life insurance premium for 52 year old female, $2,000,000 coverage, Preferred rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $2,000,000
• Duration: Lifetime Coverage
• Issue Age: 52
• Sex: Female
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_52): 0.001852
• Underwriting Multiplier: 0.75x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 90% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $7779.95
• Expense Charge: $1944.99
• Reserve Accumulation: $2593.32
• Profit Margin: $648.33
• Gross Annual Premium: $12966.59

PAYMENT OPTIONS:
• Annual: $12966.59
• Semi-Annual: $6742.63 (x2 = $13485.25/year)
• Quarterly: $3436.15 (x4 = $13744.58/year)
• Monthly: $1166.99 (x12 = $14003.91/year)

RESERVE CALCULATIONS:
• Net Level Premium: $9724.94
• First Year Reserve: $2593.32
• Terminal Reserve (Year 13): $1373850.85

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

Internal Rate of Return: 12.0%
Profit Margin: 13.7%
Lapse Assumption: 6.0% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Whole Life life insurance premium for 52 year old female, $2,000,000 coverage, Preferred 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: 52
• Sex: Female
• Underwriting Class: Preferred

PREMIUM COMPUTATION:
• Base Mortality Rate (q_52): 0.001852
• Underwriting Multiplier: 0.75x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 90% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $7779.95
• Expense Charge: $1944.99
• Reserve Accumulation: $2593.32
• Profit Margin: $648.33
• Gross Annual Premium: $12966.59

PAYMENT OPTIONS:
• Annual: $12966.59
• Semi-Annual: $6742.63 (x2 = $13485.25/year)
• Quarterly: $3436.15 (x4 = $13744.58/year)
• Monthly: $1166.99 (x12 = $14003.91/year)

RESERVE CALCULATIONS:
• Net Level Premium: $9724.94
• First Year Reserve: $2593.32
• Terminal Reserve (Year 13): $1373850.85

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

Internal Rate of Return: 12.0%
Profit Margin: 13.7%
Lapse Assumption: 6.0% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: What is the mortality rate for Suicide in Australia for 25-44 in 2019?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Suicide
Location: Australia
Year: 2019
Age Group: 25-44

MORTALITY STATISTICS:
• Crude Death Rate: 17.1 per 100,000 population
• Age-Adjusted Rate: 15.5 per 100,000
• Total Deaths: 438,630
• Percentage of All Deaths: 24.9%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 20.6 per 100,000
• Female Death Rate: 14.6 per 100,000
• Sex Ratio (M:F): 1.48:1

TREND ANALYSIS:
• 5-Year Change: +9.5%
• 10-Year Change: +22.6%
• Annual Percentage Change: +0.9%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #8
• Years of Potential Life Lost (YPLL): 6988771
• Economic Burden: $90.9 billion annually
• Preventable Deaths: 51%

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

International Classification of Diseases (ICD-10): X60-X84
Data Quality: Partial (96% coverage)

Human: What is the mortality rate for Suicide in Australia for 25-44 in 2019?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Suicide
Location: Australia
Year: 2019
Age Group: 25-44

MORTALITY STATISTICS:
• Crude Death Rate: 17.1 per 100,000 population
• Age-Adjusted Rate: 15.5 per 100,000
• Total Deaths: 438,630
• Percentage of All Deaths: 24.9%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 20.6 per 100,000
• Female Death Rate: 14.6 per 100,000
• Sex Ratio (M:F): 1.48:1

TREND ANALYSIS:
• 5-Year Change: +9.5%
• 10-Year Change: +22.6%
• Annual Percentage Change: +0.9%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #8
• Years of Potential Life Lost (YPLL): 6988771
• Economic Burden: $90.9 billion annually
• Preventable Deaths: 51%

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

International Classification of Diseases (ICD-10): X60-X84
Data Quality: Partial (96% coverage)


Instruction: Analyze mortality differences by education in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Education
Country: USA
Analysis Period: 2023

MORTALITY RATES BY EDUCATION (per 100,000):
• Less than High School: 280.1
• High School: 747.4
• Some College: 833.5
• Bachelor's: 244.3
• Graduate Degree: 1195.3

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.46
• Rate Difference: 788.0 per 100,000
• Population Attributable Risk: 36.2%
• Gini Coefficient: 0.376

LIFE EXPECTANCY BY EDUCATION:
• Less than High School: 79.8 years
• High School: 76.8 years
• Some College: 72.5 years
• Bachelor's: 83.3 years
• Graduate Degree: 81.0 years

CONTRIBUTING FACTORS:
• Healthcare Access: 37% of disparity
• Socioeconomic Status: 22% of disparity
• Environmental Factors: 22% of disparity
• Behavioral Factors: 22% of disparity
• Biological Factors: 12% of disparity

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

Social determinants explain 72% of observed mortality differences.

Human: Analyze mortality differences by education in the USA

Actuarial AI: DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Education
Country: USA
Analysis Period: 2023

MORTALITY RATES BY EDUCATION (per 100,000):
• Less than High School: 280.1
• High School: 747.4
• Some College: 833.5
• Bachelor's: 244.3
• Graduate Degree: 1195.3

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.46
• Rate Difference: 788.0 per 100,000
• Population Attributable Risk: 36.2%
• Gini Coefficient: 0.376

LIFE EXPECTANCY BY EDUCATION:
• Less than High School: 79.8 years
• High School: 76.8 years
• Some College: 72.5 years
• Bachelor's: 83.3 years
• Graduate Degree: 81.0 years

CONTRIBUTING FACTORS:
• Healthcare Access: 37% of disparity
• Socioeconomic Status: 22% of disparity
• Environmental Factors: 22% of disparity
• Behavioral Factors: 22% of disparity
• Biological Factors: 12% of disparity

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

Social determinants explain 72% of observed mortality differences.