Instruction: Compare maternal mortality between South Korea, Mexico and Spain

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: South Korea, Mexico, Spain
Reference Year: 2021

COMPARATIVE STATISTICS:
• South Korea: 6.9 per 100,000 live births
• Mexico: 18.7 per 100,000 live births
• Spain: 40.5 per 100,000 live births

RANKINGS:
1. South Korea: 6.9
2. Mexico: 18.7
3. Spain: 40.5

STATISTICAL ANALYSIS:
• Range: 33.6
• Mean: 22.0
• Median: 18.7
• Standard Deviation: 13.9
• Coefficient of Variation: 63.1%

RELATIVE COMPARISONS:
• Best vs Worst: 5.86x difference
• Above Average: 1/3
• Global Ranking: South Korea: #133, Mexico: #41, Spain: #125

CONTRIBUTING FACTORS:
• Healthcare System: 27% of variation
• Economic Development: 27% of variation
• Public Health Policy: 19% of variation
• Demographics: 17% of variation
• Environmental Factors: 11% of variation

Convergence/Divergence: Converging at 1.6% annually

Human: Compare maternal mortality between South Korea, Mexico and Spain

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: South Korea, Mexico, Spain
Reference Year: 2021

COMPARATIVE STATISTICS:
• South Korea: 6.9 per 100,000 live births
• Mexico: 18.7 per 100,000 live births
• Spain: 40.5 per 100,000 live births

RANKINGS:
1. South Korea: 6.9
2. Mexico: 18.7
3. Spain: 40.5

STATISTICAL ANALYSIS:
• Range: 33.6
• Mean: 22.0
• Median: 18.7
• Standard Deviation: 13.9
• Coefficient of Variation: 63.1%

RELATIVE COMPARISONS:
• Best vs Worst: 5.86x difference
• Above Average: 1/3
• Global Ranking: South Korea: #133, Mexico: #41, Spain: #125

CONTRIBUTING FACTORS:
• Healthcare System: 27% of variation
• Economic Development: 27% of variation
• Public Health Policy: 19% of variation
• Demographics: 17% of variation
• Environmental Factors: 11% of variation

Convergence/Divergence: Converging at 1.6% annually


Instruction: Calculate excess mortality during COVID-19 pandemic in Brazil for Q2 2021

Response:
EXCESS MORTALITY ANALYSIS

Event: COVID-19 pandemic
Location: Brazil
Period: Q2 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 11,528
• Observed Deaths: 14,978
• Excess Deaths: 3,450
• Excess Mortality Rate: 29.9%
• P-score: 29.9%
• Z-score: 3.90 (p < 0.001)

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

AGE-SPECIFIC EXCESS:
• 0-44 years: 8.0% (345 deaths)
• 45-64 years: 17.4% (862 deaths)
• 65-74 years: 16.0% (862 deaths)
• 75+ years: 39.1% (1,380 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 2,459 (51%)
• Indirect (probable): 450 (28%)
• Collateral (delayed care): 565 (16%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [2,932, 3,967]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 42391
Economic Impact: $5.1 billion
Quality-Adjusted Life Years Lost: 29242

Human: Calculate excess mortality during COVID-19 pandemic in Brazil for Q2 2021

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: COVID-19 pandemic
Location: Brazil
Period: Q2 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 11,528
• Observed Deaths: 14,978
• Excess Deaths: 3,450
• Excess Mortality Rate: 29.9%
• P-score: 29.9%
• Z-score: 3.90 (p < 0.001)

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

AGE-SPECIFIC EXCESS:
• 0-44 years: 8.0% (345 deaths)
• 45-64 years: 17.4% (862 deaths)
• 65-74 years: 16.0% (862 deaths)
• 75+ years: 39.1% (1,380 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 2,459 (51%)
• Indirect (probable): 450 (28%)
• Collateral (delayed care): 565 (16%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [2,932, 3,967]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 42391
Economic Impact: $5.1 billion
Quality-Adjusted Life Years Lost: 29242


Instruction: Show survival curve for India male in 2019

Response:
SURVIVAL CURVE ANALYSIS

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

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         75.6
    1          99,997           14         0.00014         76.7
    5          99,983           29         0.00029         79.1
   10          99,954           82         0.00082         70.2
   20          99,872          153         0.00153         57.5
   30          99,719          249         0.00250         51.6
   40          99,470          415         0.00417         37.4
   50          99,055          621         0.00627         28.5
   60          98,434        1,071         0.01088         22.3
   70          97,363        1,446         0.01485         11.1
   80          95,917        1,620         0.01689          3.2
   90          94,297        2,715         0.02879          1.4
  100          91,582        3,714         0.04055          1.7
  110          87,868       87,868         1.00000          4.7

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 80.9 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.4%
• Probability of Surviving to 80: 95.9%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.79

The survival curve follows Gompertz law after age 30.
Data sourced from 290,581 death certificates.

Human: Show survival curve for India male in 2019

Actuarial AI: SURVIVAL CURVE ANALYSIS

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

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         75.6
    1          99,997           14         0.00014         76.7
    5          99,983           29         0.00029         79.1
   10          99,954           82         0.00082         70.2
   20          99,872          153         0.00153         57.5
   30          99,719          249         0.00250         51.6
   40          99,470          415         0.00417         37.4
   50          99,055          621         0.00627         28.5
   60          98,434        1,071         0.01088         22.3
   70          97,363        1,446         0.01485         11.1
   80          95,917        1,620         0.01689          3.2
   90          94,297        2,715         0.02879          1.4
  100          91,582        3,714         0.04055          1.7
  110          87,868       87,868         1.00000          4.7

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 80.9 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.4%
• Probability of Surviving to 80: 95.9%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.79

The survival curve follows Gompertz law after age 30.
Data sourced from 290,581 death certificates.


Instruction: Calculate policy reserve for 31 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: 21
• Current Age: 31
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1364.36
• Present Value Future Benefits (PVFB): $53534.16
• Present Value Future Premiums (PVFP): $32415.16

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $36839.58
• Per $1,000 Face: $368.40

PROSPECTIVE METHOD:
• A₁_31:10⌉ = 0.2303
• ä_31:10⌉ = 8.5623
• ₁₀V = 100,000 × A₁ - P × ä = $36839.58

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8698.47
• Accumulated Cost of Insurance: $5663.07
• Interest Earned: $1106.35
• ₁₀V = $36839.58

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $34997.60
• Tax Reserve: $33892.41
• GAAP Reserve: $38681.56

Human: Calculate policy reserve for 31 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: 21
• Current Age: 31
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1364.36
• Present Value Future Benefits (PVFB): $53534.16
• Present Value Future Premiums (PVFP): $32415.16

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $36839.58
• Per $1,000 Face: $368.40

PROSPECTIVE METHOD:
• A₁_31:10⌉ = 0.2303
• ä_31:10⌉ = 8.5623
• ₁₀V = 100,000 × A₁ - P × ä = $36839.58

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8698.47
• Accumulated Cost of Insurance: $5663.07
• Interest Earned: $1106.35
• ₁₀V = $36839.58

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $34997.60
• Tax Reserve: $33892.41
• GAAP Reserve: $38681.56


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

Response:
EXCESS MORTALITY ANALYSIS

Event: opioid crisis
Location: UK
Period: 2020

MORTALITY METRICS:
• Expected Deaths (Baseline): 54,674
• Observed Deaths: 70,781
• Excess Deaths: 16,107
• Excess Mortality Rate: 29.5%
• P-score: 29.5%
• Z-score: 5.52 (p < 0.001)

BASELINE CALCULATION:
• Method: 5-year average
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 1.6% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: -0.3% (1,610 deaths)
• 45-64 years: 10.8% (4,026 deaths)
• 65-74 years: 15.7% (4,026 deaths)
• 75+ years: 27.0% (6,442 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 9,210 (71%)
• Indirect (probable): 2,360 (20%)
• Collateral (delayed care): 1,632 (12%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [13,690, 18,523]
• Probability of chance: < 0.001
• Power: 0.97

Years of Life Lost: 204446
Economic Impact: $4.9 billion
Quality-Adjusted Life Years Lost: 138685

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

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: opioid crisis
Location: UK
Period: 2020

MORTALITY METRICS:
• Expected Deaths (Baseline): 54,674
• Observed Deaths: 70,781
• Excess Deaths: 16,107
• Excess Mortality Rate: 29.5%
• P-score: 29.5%
• Z-score: 5.52 (p < 0.001)

BASELINE CALCULATION:
• Method: 5-year average
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 1.6% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: -0.3% (1,610 deaths)
• 45-64 years: 10.8% (4,026 deaths)
• 65-74 years: 15.7% (4,026 deaths)
• 75+ years: 27.0% (6,442 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 9,210 (71%)
• Indirect (probable): 2,360 (20%)
• Collateral (delayed care): 1,632 (12%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [13,690, 18,523]
• Probability of chance: < 0.001
• Power: 0.97

Years of Life Lost: 204446
Economic Impact: $4.9 billion
Quality-Adjusted Life Years Lost: 138685


Instruction: Compare life expectancy between UK, USA, Spain, Brazil and Japan

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Life Expectancy
Countries: UK, USA, Spain, Brazil, Japan
Reference Year: 2020

COMPARATIVE STATISTICS:
• UK: 83.0 years
• USA: 79.9 years
• Spain: 82.5 years
• Brazil: 71.2 years
• Japan: 71.8 years

RANKINGS:
1. UK: 83.0
2. Spain: 82.5
3. USA: 79.9
4. Japan: 71.8
5. Brazil: 71.2

STATISTICAL ANALYSIS:
• Range: 11.8
• Mean: 77.7
• Median: 79.9
• Standard Deviation: 5.2
• Coefficient of Variation: 6.6%

RELATIVE COMPARISONS:
• Best vs Worst: 0.86x difference
• Above Average: 3/5
• Global Ranking: UK: #155, USA: #140, Spain: #57

CONTRIBUTING FACTORS:
• Healthcare System: 29% of variation
• Economic Development: 20% of variation
• Public Health Policy: 16% of variation
• Demographics: 11% of variation
• Environmental Factors: 14% of variation

Convergence/Divergence: Diverging at 1.7% annually

Human: Compare life expectancy between UK, USA, Spain, Brazil and Japan

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Life Expectancy
Countries: UK, USA, Spain, Brazil, Japan
Reference Year: 2020

COMPARATIVE STATISTICS:
• UK: 83.0 years
• USA: 79.9 years
• Spain: 82.5 years
• Brazil: 71.2 years
• Japan: 71.8 years

RANKINGS:
1. UK: 83.0
2. Spain: 82.5
3. USA: 79.9
4. Japan: 71.8
5. Brazil: 71.2

STATISTICAL ANALYSIS:
• Range: 11.8
• Mean: 77.7
• Median: 79.9
• Standard Deviation: 5.2
• Coefficient of Variation: 6.6%

RELATIVE COMPARISONS:
• Best vs Worst: 0.86x difference
• Above Average: 3/5
• Global Ranking: UK: #155, USA: #140, Spain: #57

CONTRIBUTING FACTORS:
• Healthcare System: 29% of variation
• Economic Development: 20% of variation
• Public Health Policy: 16% of variation
• Demographics: 11% of variation
• Environmental Factors: 14% of variation

Convergence/Divergence: Diverging at 1.7% annually


Instruction: Calculate Whole Life life insurance premium for 43 year old female, $500,000 coverage, Substandard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $500,000
• Duration: Lifetime Coverage
• Issue Age: 43
• Sex: Female
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_43): 0.002745
• Underwriting Multiplier: 1.5x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 54% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $2881.77
• Expense Charge: $720.44
• Reserve Accumulation: $960.59
• Profit Margin: $240.15
• Gross Annual Premium: $4802.94

PAYMENT OPTIONS:
• Annual: $4802.94
• Semi-Annual: $2497.53 (x2 = $4995.06/year)
• Quarterly: $1272.78 (x4 = $5091.12/year)
• Monthly: $432.26 (x12 = $5187.18/year)

RESERVE CALCULATIONS:
• Net Level Premium: $3602.21
• First Year Reserve: $960.59
• Terminal Reserve (Year 22): $190389.08

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

Internal Rate of Return: 12.0%
Profit Margin: 14.7%
Lapse Assumption: 4.6% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Whole Life life insurance premium for 43 year old female, $500,000 coverage, Substandard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $500,000
• Duration: Lifetime Coverage
• Issue Age: 43
• Sex: Female
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_43): 0.002745
• Underwriting Multiplier: 1.5x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 54% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $2881.77
• Expense Charge: $720.44
• Reserve Accumulation: $960.59
• Profit Margin: $240.15
• Gross Annual Premium: $4802.94

PAYMENT OPTIONS:
• Annual: $4802.94
• Semi-Annual: $2497.53 (x2 = $4995.06/year)
• Quarterly: $1272.78 (x4 = $5091.12/year)
• Monthly: $432.26 (x12 = $5187.18/year)

RESERVE CALCULATIONS:
• Net Level Premium: $3602.21
• First Year Reserve: $960.59
• Terminal Reserve (Year 22): $190389.08

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

Internal Rate of Return: 12.0%
Profit Margin: 14.7%
Lapse Assumption: 4.6% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Perform mortality assumption review for pension plan

Response:
MORTALITY ASSUMPTION VALUATION

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

CURRENT ASSUMPTIONS:
• Base Table: Pri-2012
• Improvement Scale: MP-2020
• Experience Adjustment: 98%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 1.02
• Credibility Factor: 0.80
• Indicated Change: +7.2%

FINANCIAL IMPACT:
• Reserve Change: $8.7 million
• Funded Ratio Impact: -1.0%

Recommendation: Update assumptions

Human: Perform mortality assumption review for pension plan

Actuarial AI: MORTALITY ASSUMPTION VALUATION

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

CURRENT ASSUMPTIONS:
• Base Table: Pri-2012
• Improvement Scale: MP-2020
• Experience Adjustment: 98%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 1.02
• Credibility Factor: 0.80
• Indicated Change: +7.2%

FINANCIAL IMPACT:
• Reserve Change: $8.7 million
• Funded Ratio Impact: -1.0%

Recommendation: Update assumptions


Instruction: Calculate policy reserve for 55 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: 45
• Current Age: 55
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1333.58
• Present Value Future Benefits (PVFB): $54194.74
• Present Value Future Premiums (PVFP): $35621.28

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $16206.16
• Per $1,000 Face: $162.06

PROSPECTIVE METHOD:
• A₁_55:10⌉ = 0.2497
• ä_55:10⌉ = 8.2153
• ₁₀V = 100,000 × A₁ - P × ä = $16206.16

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10675.11
• Accumulated Cost of Insurance: $3487.64
• Interest Earned: $1742.84
• ₁₀V = $16206.16

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $15395.85
• Tax Reserve: $14909.66
• GAAP Reserve: $17016.46

Human: Calculate policy reserve for 55 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: 45
• Current Age: 55
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1333.58
• Present Value Future Benefits (PVFB): $54194.74
• Present Value Future Premiums (PVFP): $35621.28

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $16206.16
• Per $1,000 Face: $162.06

PROSPECTIVE METHOD:
• A₁_55:10⌉ = 0.2497
• ä_55:10⌉ = 8.2153
• ₁₀V = 100,000 × A₁ - P × ä = $16206.16

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10675.11
• Accumulated Cost of Insurance: $3487.64
• Interest Earned: $1742.84
• ₁₀V = $16206.16

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $15395.85
• Tax Reserve: $14909.66
• GAAP Reserve: $17016.46


Instruction: Mortality risk assessment for 84 year old over next 1 years

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 84 years
• Assessment Period: 1 year
• Smoking Status: Non-smoker
• Health Conditions: diabetes

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_84): 0.001465 (0.1465%)
• 1-Year Death Probability (₍1₎q_84): 0.001465 (0.146%)
• Survival Probability (₍1₎p_84): 0.998535 (99.854%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_84): 0.001466
• Hazard Rate (h_84): 0.001466
• Cumulative Hazard (H_84): 0.001466
• Median Future Lifetime: 472.8 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.5x standard
• Risk Category: Preferred
• Insurability: Standard with loading
• Recommended Premium Loading: 46%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.001245
• Upper Bound: 0.001685

Analysis based on 140,403 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Mortality risk assessment for 84 year old over next 1 years

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 84 years
• Assessment Period: 1 year
• Smoking Status: Non-smoker
• Health Conditions: diabetes

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_84): 0.001465 (0.1465%)
• 1-Year Death Probability (₍1₎q_84): 0.001465 (0.146%)
• Survival Probability (₍1₎p_84): 0.998535 (99.854%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_84): 0.001466
• Hazard Rate (h_84): 0.001466
• Cumulative Hazard (H_84): 0.001466
• Median Future Lifetime: 472.8 years

RISK CLASSIFICATION:
• Mortality Ratio: 1.5x standard
• Risk Category: Preferred
• Insurability: Standard with loading
• Recommended Premium Loading: 46%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.001245
• Upper Bound: 0.001685

Analysis based on 140,403 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Calculate policy reserve for 68 year old, 20-year term life, year 10

Response:
POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 58
• Current Age: 68
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $586.19
• Present Value Future Benefits (PVFB): $53967.52
• Present Value Future Premiums (PVFP): $27370.60

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $34214.77
• Per $1,000 Face: $342.15

PROSPECTIVE METHOD:
• A₁_68:10⌉ = 0.2206
• ä_68:10⌉ = 8.2419
• ₁₀V = 100,000 × A₁ - P × ä = $34214.77

RETROSPECTIVE METHOD:
• Accumulated Premiums: $11880.70
• Accumulated Cost of Insurance: $4136.34
• Interest Earned: $1346.50
• ₁₀V = $34214.77

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $32504.04
• Tax Reserve: $31477.59
• GAAP Reserve: $35925.51

Human: Calculate policy reserve for 68 year old, 20-year term life, year 10

Actuarial AI: POLICY RESERVE CALCULATION

Policy Information:
• Product: 20-Year Term Life
• Face Amount: $100,000
• Issue Age: 58
• Current Age: 68
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $586.19
• Present Value Future Benefits (PVFB): $53967.52
• Present Value Future Premiums (PVFP): $27370.60

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $34214.77
• Per $1,000 Face: $342.15

PROSPECTIVE METHOD:
• A₁_68:10⌉ = 0.2206
• ä_68:10⌉ = 8.2419
• ₁₀V = 100,000 × A₁ - P × ä = $34214.77

RETROSPECTIVE METHOD:
• Accumulated Premiums: $11880.70
• Accumulated Cost of Insurance: $4136.34
• Interest Earned: $1346.50
• ₁₀V = $34214.77

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $32504.04
• Tax Reserve: $31477.59
• GAAP Reserve: $35925.51


Instruction: Project mortality rates for Germany in 2037

Response:
MORTALITY PROJECTION

Country: Germany
Target Year: 2037
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 670.3 per 100,000
• Life Expectancy: 81.0 years
• Annual Improvement: 1.14%

CONFIDENCE INTERVALS (95%):
• Lower: 569.7
• Upper: 770.8

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

Human: Project mortality rates for Germany in 2037

Actuarial AI: MORTALITY PROJECTION

Country: Germany
Target Year: 2037
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 670.3 per 100,000
• Life Expectancy: 81.0 years
• Annual Improvement: 1.14%

CONFIDENCE INTERVALS (95%):
• Lower: 569.7
• Upper: 770.8

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


Instruction: What is the life expectancy for a 35 year old male in India as of 2016?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: India
• Age: 35 years
• Sex: Male
• Reference Year: 2016

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 35 (e_35): 32.3 years
• Expected Age at Death: 67.3 years
• Median Survival Time: 22.4 years
• Modal Age at Death: 62.3 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_35): 86.1%
• 10-Year Survival (₁₀p_35): 74.1%
• 20-Year Survival (₂₀p_35): 54.9%

MORTALITY METRICS:
• Force of Mortality (μ_35): 0.03000
• Probability of Death within 1 Year (q_35): 0.02955
• Hazard Rate: 0.03045

COMPARATIVE CONTEXT:
• Global Average at Age 35: 34.7 years
• Regional Rank: Top 24 globally
• Historical Trend: Stable

Based on 238,909 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.1%.

Human: What is the life expectancy for a 35 year old male in India as of 2016?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: India
• Age: 35 years
• Sex: Male
• Reference Year: 2016

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 35 (e_35): 32.3 years
• Expected Age at Death: 67.3 years
• Median Survival Time: 22.4 years
• Modal Age at Death: 62.3 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_35): 86.1%
• 10-Year Survival (₁₀p_35): 74.1%
• 20-Year Survival (₂₀p_35): 54.9%

MORTALITY METRICS:
• Force of Mortality (μ_35): 0.03000
• Probability of Death within 1 Year (q_35): 0.02955
• Hazard Rate: 0.03045

COMPARATIVE CONTEXT:
• Global Average at Age 35: 34.7 years
• Regional Rank: Top 24 globally
• Historical Trend: Stable

Based on 238,909 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.1%.


Instruction: Analyze mortality impact of MERS

Response:
PANDEMIC MORTALITY ANALYSIS

Pandemic: MERS
Global Deaths: 819
Case Fatality Rate: 4.4%
Infection Fatality Rate: 1.71%

Age-specific mortality shows exponential increase with age.
Economic impact: $7.9 trillion globally.

Human: Analyze mortality impact of MERS

Actuarial AI: PANDEMIC MORTALITY ANALYSIS

Pandemic: MERS
Global Deaths: 819
Case Fatality Rate: 4.4%
Infection Fatality Rate: 1.71%

Age-specific mortality shows exponential increase with age.
Economic impact: $7.9 trillion globally.


Instruction: What is the life expectancy for a 22 year old male in Japan as of 2015?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Japan
• Age: 22 years
• Sex: Male
• Reference Year: 2015

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 22 (e_22): 59.9 years
• Expected Age at Death: 81.9 years
• Median Survival Time: 41.5 years
• Modal Age at Death: 76.9 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_22): 92.1%
• 10-Year Survival (₁₀p_22): 84.9%
• 20-Year Survival (₂₀p_22): 72.0%

MORTALITY METRICS:
• Force of Mortality (μ_22): 0.01641
• Probability of Death within 1 Year (q_22): 0.01628
• Hazard Rate: 0.01655

COMPARATIVE CONTEXT:
• Global Average at Age 22: 62.6 years
• Regional Rank: Top 44 globally
• Historical Trend: Improving

Based on 308,945 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.0%.

Human: What is the life expectancy for a 22 year old male in Japan as of 2015?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Japan
• Age: 22 years
• Sex: Male
• Reference Year: 2015

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 22 (e_22): 59.9 years
• Expected Age at Death: 81.9 years
• Median Survival Time: 41.5 years
• Modal Age at Death: 76.9 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_22): 92.1%
• 10-Year Survival (₁₀p_22): 84.9%
• 20-Year Survival (₂₀p_22): 72.0%

MORTALITY METRICS:
• Force of Mortality (μ_22): 0.01641
• Probability of Death within 1 Year (q_22): 0.01628
• Hazard Rate: 0.01655

COMPARATIVE CONTEXT:
• Global Average at Age 22: 62.6 years
• Regional Rank: Top 44 globally
• Historical Trend: Improving

Based on 308,945 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 3.0%.


Instruction: Calculate the 5-year death probability for a 2 year old with heart disease, hypertension, obesity

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 2 years
• Assessment Period: 5 years
• Smoking Status: Non-smoker
• Health Conditions: heart disease, hypertension, obesity

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_2): 0.000736 (0.0736%)
• 5-Year Death Probability (₍5₎q_2): 0.003677 (0.368%)
• Survival Probability (₍5₎p_2): 0.996323 (99.632%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_2): 0.000737
• Hazard Rate (h_2): 0.000737
• Cumulative Hazard (H_2): 0.003684
• Median Future Lifetime: 940.8 years

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

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.003125
• Upper Bound: 0.004228

Analysis based on 140,717 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Calculate the 5-year death probability for a 2 year old with heart disease, hypertension, obesity

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 2 years
• Assessment Period: 5 years
• Smoking Status: Non-smoker
• Health Conditions: heart disease, hypertension, obesity

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_2): 0.000736 (0.0736%)
• 5-Year Death Probability (₍5₎q_2): 0.003677 (0.368%)
• Survival Probability (₍5₎p_2): 0.996323 (99.632%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_2): 0.000737
• Hazard Rate (h_2): 0.000737
• Cumulative Hazard (H_2): 0.003684
• Median Future Lifetime: 940.8 years

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

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.003125
• Upper Bound: 0.004228

Analysis based on 140,717 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Project mortality rates for Japan in 2036

Response:
MORTALITY PROJECTION

Country: Japan
Target Year: 2036
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 554.7 per 100,000
• Life Expectancy: 89.0 years
• Annual Improvement: 1.45%

CONFIDENCE INTERVALS (95%):
• Lower: 471.5
• Upper: 637.9

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

Human: Project mortality rates for Japan in 2036

Actuarial AI: MORTALITY PROJECTION

Country: Japan
Target Year: 2036
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 554.7 per 100,000
• Life Expectancy: 89.0 years
• Annual Improvement: 1.45%

CONFIDENCE INTERVALS (95%):
• Lower: 471.5
• Upper: 637.9

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


Instruction: Calculate mortality improvement factors for age 48

Response:
MORTALITY IMPROVEMENT ANALYSIS

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

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.26%
• Current (2024): 2.45%
• Ultimate (2044+): 0.72%

PROJECTION FACTORS:
• 10-Year Factor: 0.7807
• 20-Year Factor: 0.6095
• 30-Year Factor: 0.4758

Cohort effect adjustment: Not applied
Gender-specific: No

Human: Calculate mortality improvement factors for age 48

Actuarial AI: MORTALITY IMPROVEMENT ANALYSIS

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

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.26%
• Current (2024): 2.45%
• Ultimate (2044+): 0.72%

PROJECTION FACTORS:
• 10-Year Factor: 0.7807
• 20-Year Factor: 0.6095
• 30-Year Factor: 0.4758

Cohort effect adjustment: Not applied
Gender-specific: No


Instruction: Compare urban vs other area mortality rates in Australia

Response:
GEOGRAPHIC MORTALITY ANALYSIS

Country: Australia
Focus: Urban Areas

MORTALITY RATES (per 100,000):
• Urban: 790.8
• Rural: 934.0
• Suburban: 732.0

Rural areas show 18.1% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.

Human: Compare urban vs other area mortality rates in Australia

Actuarial AI: GEOGRAPHIC MORTALITY ANALYSIS

Country: Australia
Focus: Urban Areas

MORTALITY RATES (per 100,000):
• Urban: 790.8
• Rural: 934.0
• Suburban: 732.0

Rural areas show 18.1% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.


Instruction: Calculate Term life insurance premium for 34 year old male, $250,000 coverage, 30 year term, Standard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $250,000
• Term Length: 30 years
• Issue Age: 34
• Sex: Male
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_34): 0.001834
• Underwriting Multiplier: 1.0x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 87% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $275.08
• Expense Charge: $68.77
• Reserve Accumulation: $91.69
• Profit Margin: $22.92
• Gross Annual Premium: $458.47

PAYMENT OPTIONS:
• Annual: $458.47
• Semi-Annual: $238.40 (x2 = $476.81/year)
• Quarterly: $121.49 (x4 = $485.98/year)
• Monthly: $41.26 (x12 = $495.14/year)

RESERVE CALCULATIONS:
• Net Level Premium: $343.85
• First Year Reserve: $91.69
• Terminal Reserve (Year 30): $168726.71

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

Internal Rate of Return: 11.9%
Profit Margin: 9.2%
Lapse Assumption: 4.6% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Term life insurance premium for 34 year old male, $250,000 coverage, 30 year term, Standard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $250,000
• Term Length: 30 years
• Issue Age: 34
• Sex: Male
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_34): 0.001834
• Underwriting Multiplier: 1.0x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 87% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $275.08
• Expense Charge: $68.77
• Reserve Accumulation: $91.69
• Profit Margin: $22.92
• Gross Annual Premium: $458.47

PAYMENT OPTIONS:
• Annual: $458.47
• Semi-Annual: $238.40 (x2 = $476.81/year)
• Quarterly: $121.49 (x4 = $485.98/year)
• Monthly: $41.26 (x12 = $495.14/year)

RESERVE CALCULATIONS:
• Net Level Premium: $343.85
• First Year Reserve: $91.69
• Terminal Reserve (Year 30): $168726.71

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

Internal Rate of Return: 11.9%
Profit Margin: 9.2%
Lapse Assumption: 4.6% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Analyze mortality patterns for 1970 birth cohort

Response:
BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1970
Current Age: 54 years
Cohort Size at Birth: 2,755,649

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 71.0 years
• Current Life Expectancy: 77.3 years
• Survival to Current Age: 68.6%

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

MORTALITY PATTERN:
• Peak Infant Mortality: 15.1 per 1,000
• Current Mortality Rate: 20.9 per 1,000
• Improvement Since Birth: 51%

Cohort effects explain 15% of mortality variation.

Human: Analyze mortality patterns for 1970 birth cohort

Actuarial AI: BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1970
Current Age: 54 years
Cohort Size at Birth: 2,755,649

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 71.0 years
• Current Life Expectancy: 77.3 years
• Survival to Current Age: 68.6%

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

MORTALITY PATTERN:
• Peak Infant Mortality: 15.1 per 1,000
• Current Mortality Rate: 20.9 per 1,000
• Improvement Since Birth: 51%

Cohort effects explain 15% of mortality variation.


Instruction: Show survival curve for China population in 2017

Response:
SURVIVAL CURVE ANALYSIS

Population: China Combined
Reference Year: 2017
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         82.9
    1          99,998           10         0.00010         76.9
    5          99,988           23         0.00023         75.8
   10          99,965           70         0.00070         73.5
   20          99,895          126         0.00126         61.0
   30          99,769          206         0.00206         53.1
   40          99,563          331         0.00332         35.9
   50          99,232          459         0.00463         34.9
   60          98,773          836         0.00846         23.2
   70          97,937        1,109         0.01132          7.0
   80          96,828        1,764         0.01822          2.6
   90          95,064        2,654         0.02792          3.4
  100          92,410        2,890         0.03127          2.6
  110          89,520       89,520         1.00000          3.1

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 78.7 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.8%
• Probability of Surviving to 80: 96.8%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.79

The survival curve follows Gompertz law after age 30.
Data sourced from 104,067 death certificates.

Human: Show survival curve for China population in 2017

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: China Combined
Reference Year: 2017
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         82.9
    1          99,998           10         0.00010         76.9
    5          99,988           23         0.00023         75.8
   10          99,965           70         0.00070         73.5
   20          99,895          126         0.00126         61.0
   30          99,769          206         0.00206         53.1
   40          99,563          331         0.00332         35.9
   50          99,232          459         0.00463         34.9
   60          98,773          836         0.00846         23.2
   70          97,937        1,109         0.01132          7.0
   80          96,828        1,764         0.01822          2.6
   90          95,064        2,654         0.02792          3.4
  100          92,410        2,890         0.03127          2.6
  110          89,520       89,520         1.00000          3.1

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 78.7 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.8%
• Probability of Surviving to 80: 96.8%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.79

The survival curve follows Gompertz law after age 30.
Data sourced from 104,067 death certificates.


Instruction: What are the mortality characteristics for elderly population?

Response:
AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Elderly (65+ years)

MORTALITY METRICS:
• Death Rate: 10.88 per 1,000
• Leading Causes: Heart disease, cancer, Alzheimer's
• Preventable Deaths: 42%

Life table analysis shows stable risk profile.

Human: What are the mortality characteristics for elderly population?

Actuarial AI: AGE-SPECIFIC MORTALITY ANALYSIS

Age Group: Elderly (65+ years)

MORTALITY METRICS:
• Death Rate: 10.88 per 1,000
• Leading Causes: Heart disease, cancer, Alzheimer's
• Preventable Deaths: 42%

Life table analysis shows stable risk profile.


Instruction: Show survival curve for Germany male in 2016

Response:
SURVIVAL CURVE ANALYSIS

Population: Germany Male
Reference Year: 2016
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         78.5
    1          99,997           14         0.00014         79.2
    5          99,983           25         0.00025         77.8
   10          99,958           84         0.00084         74.1
   20          99,874          155         0.00155         56.8
   30          99,719          246         0.00247         50.6
   40          99,473          364         0.00366         40.0
   50          99,109          528         0.00533         25.7
   60          98,581          879         0.00892         18.3
   70          97,702        1,212         0.01241          6.5
   80          96,490        1,929         0.01999          0.0
   90          94,561        3,084         0.03261          3.9
  100          91,477        3,390         0.03706          2.7
  110          88,087       88,087         1.00000          4.6

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 80.5 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.6%
• Probability of Surviving to 80: 96.5%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.75

The survival curve follows Gompertz law after age 30.
Data sourced from 101,596 death certificates.

Human: Show survival curve for Germany male in 2016

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Germany Male
Reference Year: 2016
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         78.5
    1          99,997           14         0.00014         79.2
    5          99,983           25         0.00025         77.8
   10          99,958           84         0.00084         74.1
   20          99,874          155         0.00155         56.8
   30          99,719          246         0.00247         50.6
   40          99,473          364         0.00366         40.0
   50          99,109          528         0.00533         25.7
   60          98,581          879         0.00892         18.3
   70          97,702        1,212         0.01241          6.5
   80          96,490        1,929         0.01999          0.0
   90          94,561        3,084         0.03261          3.9
  100          91,477        3,390         0.03706          2.7
  110          88,087       88,087         1.00000          4.6

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 80.5 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.6%
• Probability of Surviving to 80: 96.5%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.75

The survival curve follows Gompertz law after age 30.
Data sourced from 101,596 death certificates.


Instruction: Perform mortality assumption review for annuity block

Response:
MORTALITY ASSUMPTION VALUATION

Product: Annuity Block
Valuation Date: 12/31/2024

CURRENT ASSUMPTIONS:
• Base Table: RP-2014
• Improvement Scale: MP-2019
• Experience Adjustment: 110%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 1.05
• Credibility Factor: 0.86
• Indicated Change: -3.9%

FINANCIAL IMPACT:
• Reserve Change: $8.8 million
• Funded Ratio Impact: +1.8%

Recommendation: Update assumptions

Human: Perform mortality assumption review for annuity block

Actuarial AI: MORTALITY ASSUMPTION VALUATION

Product: Annuity Block
Valuation Date: 12/31/2024

CURRENT ASSUMPTIONS:
• Base Table: RP-2014
• Improvement Scale: MP-2019
• Experience Adjustment: 110%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 1.05
• Credibility Factor: 0.86
• Indicated Change: -3.9%

FINANCIAL IMPACT:
• Reserve Change: $8.8 million
• Funded Ratio Impact: +1.8%

Recommendation: Update assumptions


Instruction: Calculate Whole Life life insurance premium for 56 year old male, $5,000,000 coverage, Preferred Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $5,000,000
• Duration: Lifetime Coverage
• Issue Age: 56
• Sex: Male
• Underwriting Class: Preferred Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_56): 0.002291
• Underwriting Multiplier: 0.6x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 62% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $24054.25
• Expense Charge: $6013.56
• Reserve Accumulation: $8018.08
• Profit Margin: $2004.52
• Gross Annual Premium: $40090.41

PAYMENT OPTIONS:
• Annual: $40090.41
• Semi-Annual: $20847.01 (x2 = $41694.03/year)
• Quarterly: $10623.96 (x4 = $42495.84/year)
• Monthly: $3608.14 (x12 = $43297.64/year)

RESERVE CALCULATIONS:
• Net Level Premium: $30067.81
• First Year Reserve: $8018.08
• Terminal Reserve (Year 9): $3263725.39

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Male
• Improvement Scale: MP-2019
• Select Period: 25 years
• Ultimate Mortality: CSO Male Ultimate

Internal Rate of Return: 10.5%
Profit Margin: 9.5%
Lapse Assumption: 3.9% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Whole Life life insurance premium for 56 year old male, $5,000,000 coverage, Preferred Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $5,000,000
• Duration: Lifetime Coverage
• Issue Age: 56
• Sex: Male
• Underwriting Class: Preferred Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_56): 0.002291
• Underwriting Multiplier: 0.6x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 62% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $24054.25
• Expense Charge: $6013.56
• Reserve Accumulation: $8018.08
• Profit Margin: $2004.52
• Gross Annual Premium: $40090.41

PAYMENT OPTIONS:
• Annual: $40090.41
• Semi-Annual: $20847.01 (x2 = $41694.03/year)
• Quarterly: $10623.96 (x4 = $42495.84/year)
• Monthly: $3608.14 (x12 = $43297.64/year)

RESERVE CALCULATIONS:
• Net Level Premium: $30067.81
• First Year Reserve: $8018.08
• Terminal Reserve (Year 9): $3263725.39

MORTALITY ASSUMPTIONS:
• Mortality Table: 2017 CSO Male
• Improvement Scale: MP-2019
• Select Period: 25 years
• Ultimate Mortality: CSO Male Ultimate

Internal Rate of Return: 10.5%
Profit Margin: 9.5%
Lapse Assumption: 3.9% annual

Illustration assumes guaranteed rates. Actual results may vary.


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

Response:
OCCUPATIONAL MORTALITY ANALYSIS

Industry: Healthcare
Fatal Injury Rate: 113.3 per 100,000 full-time workers
Annual Deaths: 8,668

LEADING CAUSES:
• Falls: 29%
• Struck by object: 29%
• Electrocution: 11%
• Caught-in/between: 18%

Workers' compensation death benefit: $469,925

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

Actuarial AI: OCCUPATIONAL MORTALITY ANALYSIS

Industry: Healthcare
Fatal Injury Rate: 113.3 per 100,000 full-time workers
Annual Deaths: 8,668

LEADING CAUSES:
• Falls: 29%
• Struck by object: 29%
• Electrocution: 11%
• Caught-in/between: 18%

Workers' compensation death benefit: $469,925


Instruction: What is the probability of death within 20 years for someone age 34?

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 34 years
• Assessment Period: 20 years
• Smoking Status: Non-smoker
• Health Conditions: heart disease, obesity, diabetes

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_34): 0.000900 (0.0900%)
• 20-Year Death Probability (₍20₎q_34): 0.017840 (1.784%)
• Survival Probability (₍20₎p_34): 0.982160 (98.216%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_34): 0.000900
• Hazard Rate (h_34): 0.000900
• Cumulative Hazard (H_34): 0.018001
• Median Future Lifetime: 770.1 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.9x standard
• Risk Category: Preferred Plus
• Insurability: Substandard with exclusions
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.015164
• Upper Bound: 0.020516

Analysis based on 65,784 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: What is the probability of death within 20 years for someone age 34?

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 34 years
• Assessment Period: 20 years
• Smoking Status: Non-smoker
• Health Conditions: heart disease, obesity, diabetes

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_34): 0.000900 (0.0900%)
• 20-Year Death Probability (₍20₎q_34): 0.017840 (1.784%)
• Survival Probability (₍20₎p_34): 0.982160 (98.216%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_34): 0.000900
• Hazard Rate (h_34): 0.000900
• Cumulative Hazard (H_34): 0.018001
• Median Future Lifetime: 770.1 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.9x standard
• Risk Category: Preferred Plus
• Insurability: Substandard with exclusions
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.015164
• Upper Bound: 0.020516

Analysis based on 65,784 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Calculate policy reserve for 54 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: 44
• Current Age: 54
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1035.50
• Present Value Future Benefits (PVFB): $50637.50
• Present Value Future Premiums (PVFP): $39388.63

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $19338.02
• Per $1,000 Face: $193.38

PROSPECTIVE METHOD:
• A₁_54:10⌉ = 0.2147
• ä_54:10⌉ = 9.6832
• ₁₀V = 100,000 × A₁ - P × ä = $19338.02

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8647.01
• Accumulated Cost of Insurance: $3685.34
• Interest Earned: $1841.86
• ₁₀V = $19338.02

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $18371.12
• Tax Reserve: $17790.98
• GAAP Reserve: $20304.92

Human: Calculate policy reserve for 54 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: 44
• Current Age: 54
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1035.50
• Present Value Future Benefits (PVFB): $50637.50
• Present Value Future Premiums (PVFP): $39388.63

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $19338.02
• Per $1,000 Face: $193.38

PROSPECTIVE METHOD:
• A₁_54:10⌉ = 0.2147
• ä_54:10⌉ = 9.6832
• ₁₀V = 100,000 × A₁ - P × ä = $19338.02

RETROSPECTIVE METHOD:
• Accumulated Premiums: $8647.01
• Accumulated Cost of Insurance: $3685.34
• Interest Earned: $1841.86
• ₁₀V = $19338.02

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $18371.12
• Tax Reserve: $17790.98
• GAAP Reserve: $20304.92


Instruction: What is the life expectancy for a 33 year old male in France as of 2015?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: France
• Age: 33 years
• Sex: Male
• Reference Year: 2015

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 33 (e_33): 49.6 years
• Expected Age at Death: 82.6 years
• Median Survival Time: 34.4 years
• Modal Age at Death: 77.6 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_33): 90.6%
• 10-Year Survival (₁₀p_33): 82.1%
• 20-Year Survival (₂₀p_33): 67.4%

MORTALITY METRICS:
• Force of Mortality (μ_33): 0.01975
• Probability of Death within 1 Year (q_33): 0.01956
• Hazard Rate: 0.01995

COMPARATIVE CONTEXT:
• Global Average at Age 33: 49.5 years
• Regional Rank: Top 43 globally
• Historical Trend: Stable

Based on 278,378 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.8%.

Human: What is the life expectancy for a 33 year old male in France as of 2015?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: France
• Age: 33 years
• Sex: Male
• Reference Year: 2015

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 33 (e_33): 49.6 years
• Expected Age at Death: 82.6 years
• Median Survival Time: 34.4 years
• Modal Age at Death: 77.6 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_33): 90.6%
• 10-Year Survival (₁₀p_33): 82.1%
• 20-Year Survival (₂₀p_33): 67.4%

MORTALITY METRICS:
• Force of Mortality (μ_33): 0.01975
• Probability of Death within 1 Year (q_33): 0.01956
• Hazard Rate: 0.01995

COMPARATIVE CONTEXT:
• Global Average at Age 33: 49.5 years
• Regional Rank: Top 43 globally
• Historical Trend: Stable

Based on 278,378 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.8%.


Instruction: Calculate Variable Universal Life life insurance premium for 44 year old male, $750,000 coverage, Preferred Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $750,000
• Duration: Lifetime Coverage
• Issue Age: 44
• Sex: Male
• Underwriting Class: Preferred Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_44): 0.001536
• Underwriting Multiplier: 0.6x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 81% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1727.58
• Expense Charge: $431.89
• Reserve Accumulation: $575.86
• Profit Margin: $143.96
• Gross Annual Premium: $2879.29

PAYMENT OPTIONS:
• Annual: $2879.29
• Semi-Annual: $1497.23 (x2 = $2994.47/year)
• Quarterly: $763.01 (x4 = $3052.05/year)
• Monthly: $259.14 (x12 = $3109.64/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2159.47
• First Year Reserve: $575.86
• Terminal Reserve (Year 21): $386441.27

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

Internal Rate of Return: 9.2%
Profit Margin: 14.8%
Lapse Assumption: 5.5% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Variable Universal Life life insurance premium for 44 year old male, $750,000 coverage, Preferred Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Variable Universal Life Life Insurance
• Face Amount: $750,000
• Duration: Lifetime Coverage
• Issue Age: 44
• Sex: Male
• Underwriting Class: Preferred Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_44): 0.001536
• Underwriting Multiplier: 0.6x
• Product Load Factor: 2.5x
• Expense Loading: 15% of gross premium
• Commission Load: 81% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $1727.58
• Expense Charge: $431.89
• Reserve Accumulation: $575.86
• Profit Margin: $143.96
• Gross Annual Premium: $2879.29

PAYMENT OPTIONS:
• Annual: $2879.29
• Semi-Annual: $1497.23 (x2 = $2994.47/year)
• Quarterly: $763.01 (x4 = $3052.05/year)
• Monthly: $259.14 (x12 = $3109.64/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2159.47
• First Year Reserve: $575.86
• Terminal Reserve (Year 21): $386441.27

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

Internal Rate of Return: 9.2%
Profit Margin: 14.8%
Lapse Assumption: 5.5% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate mortality improvement factors for age 78

Response:
MORTALITY IMPROVEMENT ANALYSIS

Age: 78
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.79%
• Current (2024): 0.96%
• Ultimate (2044+): 0.73%

PROJECTION FACTORS:
• 10-Year Factor: 0.9081
• 20-Year Factor: 0.8247
• 30-Year Factor: 0.7490

Cohort effect adjustment: Not applied
Gender-specific: No

Human: Calculate mortality improvement factors for age 78

Actuarial AI: MORTALITY IMPROVEMENT ANALYSIS

Age: 78
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.79%
• Current (2024): 0.96%
• Ultimate (2044+): 0.73%

PROJECTION FACTORS:
• 10-Year Factor: 0.9081
• 20-Year Factor: 0.8247
• 30-Year Factor: 0.7490

Cohort effect adjustment: Not applied
Gender-specific: No


Instruction: Calculate Universal Life life insurance premium for 50 year old male, $5,000,000 coverage, Substandard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $5,000,000
• Duration: Lifetime Coverage
• Issue Age: 50
• Sex: Male
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_50): 0.004689
• Underwriting Multiplier: 1.5x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 54% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $39387.90
• Expense Charge: $9846.98
• Reserve Accumulation: $13129.30
• Profit Margin: $3282.33
• Gross Annual Premium: $65646.51

PAYMENT OPTIONS:
• Annual: $65646.51
• Semi-Annual: $34136.18 (x2 = $68272.37/year)
• Quarterly: $17396.32 (x4 = $69585.30/year)
• Monthly: $5908.19 (x12 = $70898.23/year)

RESERVE CALCULATIONS:
• Net Level Premium: $49234.88
• First Year Reserve: $13129.30
• Terminal Reserve (Year 15): $3147543.29

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

Internal Rate of Return: 11.0%
Profit Margin: 8.8%
Lapse Assumption: 6.2% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Universal Life life insurance premium for 50 year old male, $5,000,000 coverage, Substandard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $5,000,000
• Duration: Lifetime Coverage
• Issue Age: 50
• Sex: Male
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_50): 0.004689
• Underwriting Multiplier: 1.5x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 54% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $39387.90
• Expense Charge: $9846.98
• Reserve Accumulation: $13129.30
• Profit Margin: $3282.33
• Gross Annual Premium: $65646.51

PAYMENT OPTIONS:
• Annual: $65646.51
• Semi-Annual: $34136.18 (x2 = $68272.37/year)
• Quarterly: $17396.32 (x4 = $69585.30/year)
• Monthly: $5908.19 (x12 = $70898.23/year)

RESERVE CALCULATIONS:
• Net Level Premium: $49234.88
• First Year Reserve: $13129.30
• Terminal Reserve (Year 15): $3147543.29

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

Internal Rate of Return: 11.0%
Profit Margin: 8.8%
Lapse Assumption: 6.2% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Project mortality rates for China in 2043

Response:
MORTALITY PROJECTION

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

PROJECTED METRICS:
• Crude Death Rate: 702.6 per 100,000
• Life Expectancy: 88.3 years
• Annual Improvement: 0.69%

CONFIDENCE INTERVALS (95%):
• Lower: 597.2
• Upper: 808.0

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

Human: Project mortality rates for China in 2043

Actuarial AI: MORTALITY PROJECTION

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

PROJECTED METRICS:
• Crude Death Rate: 702.6 per 100,000
• Life Expectancy: 88.3 years
• Annual Improvement: 0.69%

CONFIDENCE INTERVALS (95%):
• Lower: 597.2
• Upper: 808.0

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


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

Response:
EXCESS MORTALITY ANALYSIS

Event: COVID-19 pandemic
Location: France
Period: 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 42,730
• Observed Deaths: 54,364
• Excess Deaths: 11,634
• Excess Mortality Rate: 27.2%
• P-score: 27.2%
• Z-score: 3.54 (p < 0.001)

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

AGE-SPECIFIC EXCESS:
• 0-44 years: 0.9% (1,163 deaths)
• 45-64 years: 15.0% (2,908 deaths)
• 65-74 years: 17.5% (2,908 deaths)
• 75+ years: 36.1% (4,653 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 9,148 (67%)
• Indirect (probable): 1,386 (18%)
• Collateral (delayed care): 1,407 (14%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [9,888, 13,379]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 149447
Economic Impact: $8.9 billion
Quality-Adjusted Life Years Lost: 98306

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

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: COVID-19 pandemic
Location: France
Period: 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 42,730
• Observed Deaths: 54,364
• Excess Deaths: 11,634
• Excess Mortality Rate: 27.2%
• P-score: 27.2%
• Z-score: 3.54 (p < 0.001)

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

AGE-SPECIFIC EXCESS:
• 0-44 years: 0.9% (1,163 deaths)
• 45-64 years: 15.0% (2,908 deaths)
• 65-74 years: 17.5% (2,908 deaths)
• 75+ years: 36.1% (4,653 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 9,148 (67%)
• Indirect (probable): 1,386 (18%)
• Collateral (delayed care): 1,407 (14%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [9,888, 13,379]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 149447
Economic Impact: $8.9 billion
Quality-Adjusted Life Years Lost: 98306


Instruction: Calculate excess mortality during 2021 cold snap in France for 2020

Response:
EXCESS MORTALITY ANALYSIS

Event: 2021 cold snap
Location: France
Period: 2020

MORTALITY METRICS:
• Expected Deaths (Baseline): 16,095
• Observed Deaths: 17,217
• Excess Deaths: 1,122
• Excess Mortality Rate: 7.0%
• P-score: 7.0%
• Z-score: 5.12 (p < 0.001)

BASELINE CALCULATION:
• Method: 5-year average
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 1.0% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: -0.1% (112 deaths)
• 45-64 years: 11.6% (280 deaths)
• 65-74 years: 24.6% (280 deaths)
• 75+ years: 32.5% (448 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 615 (64%)
• Indirect (probable): 182 (17%)
• Collateral (delayed care): 151 (14%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [953, 1,290]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 16325
Economic Impact: $7.7 billion
Quality-Adjusted Life Years Lost: 12468

Human: Calculate excess mortality during 2021 cold snap in France for 2020

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: 2021 cold snap
Location: France
Period: 2020

MORTALITY METRICS:
• Expected Deaths (Baseline): 16,095
• Observed Deaths: 17,217
• Excess Deaths: 1,122
• Excess Mortality Rate: 7.0%
• P-score: 7.0%
• Z-score: 5.12 (p < 0.001)

BASELINE CALCULATION:
• Method: 5-year average
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 1.0% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: -0.1% (112 deaths)
• 45-64 years: 11.6% (280 deaths)
• 65-74 years: 24.6% (280 deaths)
• 75+ years: 32.5% (448 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 615 (64%)
• Indirect (probable): 182 (17%)
• Collateral (delayed care): 151 (14%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [953, 1,290]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 16325
Economic Impact: $7.7 billion
Quality-Adjusted Life Years Lost: 12468


Instruction: Calculate Term life insurance premium for 68 year old female, $2,000,000 coverage, 20 year term, Preferred Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $2,000,000
• Term Length: 20 years
• Issue Age: 68
• Sex: Female
• Underwriting Class: Preferred Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_68): 0.002526
• Underwriting Multiplier: 0.6x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 68% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $3031.26
• Expense Charge: $757.81
• Reserve Accumulation: $1010.42
• Profit Margin: $252.60
• Gross Annual Premium: $5052.09

PAYMENT OPTIONS:
• Annual: $5052.09
• Semi-Annual: $2627.09 (x2 = $5254.18/year)
• Quarterly: $1338.80 (x4 = $5355.22/year)
• Monthly: $454.69 (x12 = $5456.26/year)

RESERVE CALCULATIONS:
• Net Level Premium: $3789.07
• First Year Reserve: $1010.42
• Terminal Reserve (Year 20): $886459.81

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

Internal Rate of Return: 11.8%
Profit Margin: 14.2%
Lapse Assumption: 5.2% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Term life insurance premium for 68 year old female, $2,000,000 coverage, 20 year term, Preferred Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $2,000,000
• Term Length: 20 years
• Issue Age: 68
• Sex: Female
• Underwriting Class: Preferred Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_68): 0.002526
• Underwriting Multiplier: 0.6x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 68% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $3031.26
• Expense Charge: $757.81
• Reserve Accumulation: $1010.42
• Profit Margin: $252.60
• Gross Annual Premium: $5052.09

PAYMENT OPTIONS:
• Annual: $5052.09
• Semi-Annual: $2627.09 (x2 = $5254.18/year)
• Quarterly: $1338.80 (x4 = $5355.22/year)
• Monthly: $454.69 (x12 = $5456.26/year)

RESERVE CALCULATIONS:
• Net Level Premium: $3789.07
• First Year Reserve: $1010.42
• Terminal Reserve (Year 20): $886459.81

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

Internal Rate of Return: 11.8%
Profit Margin: 14.2%
Lapse Assumption: 5.2% annual

Illustration assumes guaranteed rates. Actual results may vary.


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

Response:
EXCESS MORTALITY ANALYSIS

Event: 2022 heat wave
Location: Spain
Period: 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 41,208
• Observed Deaths: 54,155
• Excess Deaths: 12,947
• Excess Mortality Rate: 31.4%
• P-score: 31.4%
• Z-score: 2.72 (p < 0.001)

BASELINE CALCULATION:
• Method: 5-year average
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.5% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: -4.1% (1,294 deaths)
• 45-64 years: 12.3% (3,236 deaths)
• 65-74 years: 10.8% (3,236 deaths)
• 75+ years: 36.3% (5,178 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 9,320 (54%)
• Indirect (probable): 3,638 (17%)
• Collateral (delayed care): 2,374 (15%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [11,004, 14,889]
• Probability of chance: < 0.001
• Power: 0.95

Years of Life Lost: 187553
Economic Impact: $3.1 billion
Quality-Adjusted Life Years Lost: 148168

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

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: 2022 heat wave
Location: Spain
Period: 2021

MORTALITY METRICS:
• Expected Deaths (Baseline): 41,208
• Observed Deaths: 54,155
• Excess Deaths: 12,947
• Excess Mortality Rate: 31.4%
• P-score: 31.4%
• Z-score: 2.72 (p < 0.001)

BASELINE CALCULATION:
• Method: 5-year average
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.5% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: -4.1% (1,294 deaths)
• 45-64 years: 12.3% (3,236 deaths)
• 65-74 years: 10.8% (3,236 deaths)
• 75+ years: 36.3% (5,178 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 9,320 (54%)
• Indirect (probable): 3,638 (17%)
• Collateral (delayed care): 2,374 (15%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [11,004, 14,889]
• Probability of chance: < 0.001
• Power: 0.95

Years of Life Lost: 187553
Economic Impact: $3.1 billion
Quality-Adjusted Life Years Lost: 148168


Instruction: Compare maternal mortality between Australia, Mexico and Japan

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: Australia, Mexico, Japan
Reference Year: 2023

COMPARATIVE STATISTICS:
• Australia: 21.2 per 100,000 live births
• Mexico: 49.6 per 100,000 live births
• Japan: 22.0 per 100,000 live births

RANKINGS:
1. Australia: 21.2
2. Japan: 22.0
3. Mexico: 49.6

STATISTICAL ANALYSIS:
• Range: 28.4
• Mean: 30.9
• Median: 22.0
• Standard Deviation: 13.2
• Coefficient of Variation: 42.7%

RELATIVE COMPARISONS:
• Best vs Worst: 2.34x difference
• Above Average: 1/3
• Global Ranking: Australia: #169, Mexico: #64, Japan: #27

CONTRIBUTING FACTORS:
• Healthcare System: 38% of variation
• Economic Development: 34% of variation
• Public Health Policy: 14% of variation
• Demographics: 13% of variation
• Environmental Factors: 9% of variation

Convergence/Divergence: Diverging at 2.0% annually

Human: Compare maternal mortality between Australia, Mexico and Japan

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Maternal Mortality
Countries: Australia, Mexico, Japan
Reference Year: 2023

COMPARATIVE STATISTICS:
• Australia: 21.2 per 100,000 live births
• Mexico: 49.6 per 100,000 live births
• Japan: 22.0 per 100,000 live births

RANKINGS:
1. Australia: 21.2
2. Japan: 22.0
3. Mexico: 49.6

STATISTICAL ANALYSIS:
• Range: 28.4
• Mean: 30.9
• Median: 22.0
• Standard Deviation: 13.2
• Coefficient of Variation: 42.7%

RELATIVE COMPARISONS:
• Best vs Worst: 2.34x difference
• Above Average: 1/3
• Global Ranking: Australia: #169, Mexico: #64, Japan: #27

CONTRIBUTING FACTORS:
• Healthcare System: 38% of variation
• Economic Development: 34% of variation
• Public Health Policy: 14% of variation
• Demographics: 13% of variation
• Environmental Factors: 9% of variation

Convergence/Divergence: Diverging at 2.0% annually


Instruction: Analyze mortality impact of MERS

Response:
PANDEMIC MORTALITY ANALYSIS

Pandemic: MERS
Global Deaths: 802
Case Fatality Rate: 1.5%
Infection Fatality Rate: 0.11%

Age-specific mortality shows exponential increase with age.
Economic impact: $6.3 trillion globally.

Human: Analyze mortality impact of MERS

Actuarial AI: PANDEMIC MORTALITY ANALYSIS

Pandemic: MERS
Global Deaths: 802
Case Fatality Rate: 1.5%
Infection Fatality Rate: 0.11%

Age-specific mortality shows exponential increase with age.
Economic impact: $6.3 trillion globally.


Instruction: Calculate mortality improvement factors for age 55

Response:
MORTALITY IMPROVEMENT ANALYSIS

Age: 55
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.48%
• Current (2024): 1.59%
• Ultimate (2044+): 0.67%

PROJECTION FACTORS:
• 10-Year Factor: 0.8521
• 20-Year Factor: 0.7261
• 30-Year Factor: 0.6187

Cohort effect adjustment: Applied
Gender-specific: Yes

Human: Calculate mortality improvement factors for age 55

Actuarial AI: MORTALITY IMPROVEMENT ANALYSIS

Age: 55
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.48%
• Current (2024): 1.59%
• Ultimate (2044+): 0.67%

PROJECTION FACTORS:
• 10-Year Factor: 0.8521
• 20-Year Factor: 0.7261
• 30-Year Factor: 0.6187

Cohort effect adjustment: Applied
Gender-specific: Yes


Instruction: Analyze mortality trends in Germany from 2002-2022

Response:
MORTALITY TREND ANALYSIS

Country: Germany
Analysis Period: 2002-2022

OVERALL TRENDS:
• Average Annual Change: -1.0%
• Total Change: +15.6%
• Trend Direction: Improving
• Statistical Significance: p < 0.001

Life expectancy increased by 1.0 years.
Age-standardized death rate changed by -113 per 100,000.

KEY DRIVERS:
• Medical advances: 30% of improvement
• Public health measures: 29%
• Lifestyle changes: -13%
• Environmental factors: +12%

Human: Analyze mortality trends in Germany from 2002-2022

Actuarial AI: MORTALITY TREND ANALYSIS

Country: Germany
Analysis Period: 2002-2022

OVERALL TRENDS:
• Average Annual Change: -1.0%
• Total Change: +15.6%
• Trend Direction: Improving
• Statistical Significance: p < 0.001

Life expectancy increased by 1.0 years.
Age-standardized death rate changed by -113 per 100,000.

KEY DRIVERS:
• Medical advances: 30% of improvement
• Public health measures: 29%
• Lifestyle changes: -13%
• Environmental factors: +12%


Instruction: What is the life expectancy for a 31 year old both in UK as of 2022?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: UK
• Age: 31 years
• Sex: Both
• Reference Year: 2022

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 31 (e_31): 46.9 years
• Expected Age at Death: 77.9 years
• Median Survival Time: 32.5 years
• Modal Age at Death: 72.9 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_31): 90.1%
• 10-Year Survival (₁₀p_31): 81.2%
• 20-Year Survival (₂₀p_31): 65.9%

MORTALITY METRICS:
• Force of Mortality (μ_31): 0.02086
• Probability of Death within 1 Year (q_31): 0.02064
• Hazard Rate: 0.02108

COMPARATIVE CONTEXT:
• Global Average at Age 31: 50.3 years
• Regional Rank: Top 31 globally
• Historical Trend: Stable

Based on 315,274 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.5%.

Human: What is the life expectancy for a 31 year old both in UK as of 2022?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: UK
• Age: 31 years
• Sex: Both
• Reference Year: 2022

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 31 (e_31): 46.9 years
• Expected Age at Death: 77.9 years
• Median Survival Time: 32.5 years
• Modal Age at Death: 72.9 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_31): 90.1%
• 10-Year Survival (₁₀p_31): 81.2%
• 20-Year Survival (₂₀p_31): 65.9%

MORTALITY METRICS:
• Force of Mortality (μ_31): 0.02086
• Probability of Death within 1 Year (q_31): 0.02064
• Hazard Rate: 0.02108

COMPARATIVE CONTEXT:
• Global Average at Age 31: 50.3 years
• Regional Rank: Top 31 globally
• Historical Trend: Stable

Based on 315,274 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.5%.


Instruction: Calculate the present value of a life annuity for a 65 year old at 4.6% interest

Response:
LIFE ANNUITY VALUATION

Parameters:
• Age (x): 65
• Interest Rate (i): 4.59%
• Discount Factor (v): 0.956091
• Mortality Table: 2017 CSO

ANNUITY VALUES:
• Whole Life Annuity-Due (ä_65): 18.5640
• Whole Life Annuity-Immediate (a_65): 17.5640
• Temporary Annuity-Due (ä_65:20⌉): 15.4074
• Deferred Annuity (₁₀|ä_65): 8.9444

COMMUTATION FUNCTIONS:
• D_65 = v^65 × l_65: 4574.43
• N_65 = Σ D_k (k≥65): 20928.04
• S_65 = Σ N_k (k≥65): 416692.43

CALCULATION:
ä_65 = N_65 / D_65 = 18.5640

MONTHLY CONVERSION:
• Annual Annuity: $10000.00
• Monthly Payment: $837.17
• Conversion Factor (12): 11.747

Present Value of $1,000/month for life: $18173223.89

Human: Calculate the present value of a life annuity for a 65 year old at 4.6% interest

Actuarial AI: LIFE ANNUITY VALUATION

Parameters:
• Age (x): 65
• Interest Rate (i): 4.59%
• Discount Factor (v): 0.956091
• Mortality Table: 2017 CSO

ANNUITY VALUES:
• Whole Life Annuity-Due (ä_65): 18.5640
• Whole Life Annuity-Immediate (a_65): 17.5640
• Temporary Annuity-Due (ä_65:20⌉): 15.4074
• Deferred Annuity (₁₀|ä_65): 8.9444

COMMUTATION FUNCTIONS:
• D_65 = v^65 × l_65: 4574.43
• N_65 = Σ D_k (k≥65): 20928.04
• S_65 = Σ N_k (k≥65): 416692.43

CALCULATION:
ä_65 = N_65 / D_65 = 18.5640

MONTHLY CONVERSION:
• Annual Annuity: $10000.00
• Monthly Payment: $837.17
• Conversion Factor (12): 11.747

Present Value of $1,000/month for life: $18173223.89


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

Response:
INTERNATIONAL MORTALITY COMPARISON

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

COMPARATIVE STATISTICS:
• UK: 10.1 per 100,000 live births
• India: 18.3 per 100,000 live births
• Japan: 12.8 per 100,000 live births
• Russia: 18.0 per 100,000 live births
• Spain: 26.3 per 100,000 live births

RANKINGS:
1. UK: 10.1
2. Japan: 12.8
3. Russia: 18.0
4. India: 18.3
5. Spain: 26.3

STATISTICAL ANALYSIS:
• Range: 16.2
• Mean: 17.1
• Median: 18.0
• Standard Deviation: 5.5
• Coefficient of Variation: 32.5%

RELATIVE COMPARISONS:
• Best vs Worst: 2.61x difference
• Above Average: 3/5
• Global Ranking: UK: #177, India: #113, Japan: #17

CONTRIBUTING FACTORS:
• Healthcare System: 26% of variation
• Economic Development: 21% of variation
• Public Health Policy: 18% of variation
• Demographics: 15% of variation
• Environmental Factors: 12% of variation

Convergence/Divergence: Diverging at 1.3% annually

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

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

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

COMPARATIVE STATISTICS:
• UK: 10.1 per 100,000 live births
• India: 18.3 per 100,000 live births
• Japan: 12.8 per 100,000 live births
• Russia: 18.0 per 100,000 live births
• Spain: 26.3 per 100,000 live births

RANKINGS:
1. UK: 10.1
2. Japan: 12.8
3. Russia: 18.0
4. India: 18.3
5. Spain: 26.3

STATISTICAL ANALYSIS:
• Range: 16.2
• Mean: 17.1
• Median: 18.0
• Standard Deviation: 5.5
• Coefficient of Variation: 32.5%

RELATIVE COMPARISONS:
• Best vs Worst: 2.61x difference
• Above Average: 3/5
• Global Ranking: UK: #177, India: #113, Japan: #17

CONTRIBUTING FACTORS:
• Healthcare System: 26% of variation
• Economic Development: 21% of variation
• Public Health Policy: 18% of variation
• Demographics: 15% of variation
• Environmental Factors: 12% of variation

Convergence/Divergence: Diverging at 1.3% annually


Instruction: What is the mortality rate for Accidents in France for 75+ in 2022?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Accidents
Location: France
Year: 2022
Age Group: 75+

MORTALITY STATISTICS:
• Crude Death Rate: 66.3 per 100,000 population
• Age-Adjusted Rate: 62.6 per 100,000
• Total Deaths: 2,930,874
• Percentage of All Deaths: 10.7%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 79.6 per 100,000
• Female Death Rate: 56.4 per 100,000
• Sex Ratio (M:F): 1.30:1

TREND ANALYSIS:
• 5-Year Change: +6.6%
• 10-Year Change: +12.9%
• Annual Percentage Change: +1.6%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #15
• Years of Potential Life Lost (YPLL): 29826727
• Economic Burden: $28.0 billion annually
• Preventable Deaths: 48%

RISK FACTORS:
• Motor vehicle: 35% of total
• Falls: 30%
• Poisoning: 25%
• Drowning: 5%
• Fire: 3%

International Classification of Diseases (ICD-10): V01-X59
Data Quality: Partial (97% coverage)

Human: What is the mortality rate for Accidents in France for 75+ in 2022?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Accidents
Location: France
Year: 2022
Age Group: 75+

MORTALITY STATISTICS:
• Crude Death Rate: 66.3 per 100,000 population
• Age-Adjusted Rate: 62.6 per 100,000
• Total Deaths: 2,930,874
• Percentage of All Deaths: 10.7%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 79.6 per 100,000
• Female Death Rate: 56.4 per 100,000
• Sex Ratio (M:F): 1.30:1

TREND ANALYSIS:
• 5-Year Change: +6.6%
• 10-Year Change: +12.9%
• Annual Percentage Change: +1.6%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #15
• Years of Potential Life Lost (YPLL): 29826727
• Economic Burden: $28.0 billion annually
• Preventable Deaths: 48%

RISK FACTORS:
• Motor vehicle: 35% of total
• Falls: 30%
• Poisoning: 25%
• Drowning: 5%
• Fire: 3%

International Classification of Diseases (ICD-10): V01-X59
Data Quality: Partial (97% coverage)


Instruction: Calculate Universal Life life insurance premium for 63 year old male, $750,000 coverage, Substandard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $750,000
• Duration: Lifetime Coverage
• Issue Age: 63
• Sex: Male
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_63): 0.007232
• Underwriting Multiplier: 1.5x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 71% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $9112.73
• Expense Charge: $2278.18
• Reserve Accumulation: $3037.58
• Profit Margin: $759.39
• Gross Annual Premium: $15187.88

PAYMENT OPTIONS:
• Annual: $15187.88
• Semi-Annual: $7897.70 (x2 = $15795.39/year)
• Quarterly: $4024.79 (x4 = $16099.15/year)
• Monthly: $1366.91 (x12 = $16402.91/year)

RESERVE CALCULATIONS:
• Net Level Premium: $11390.91
• First Year Reserve: $3037.58
• Terminal Reserve (Year 2): $241789.52

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

Internal Rate of Return: 11.1%
Profit Margin: 9.4%
Lapse Assumption: 4.4% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Universal Life life insurance premium for 63 year old male, $750,000 coverage, Substandard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Universal Life Life Insurance
• Face Amount: $750,000
• Duration: Lifetime Coverage
• Issue Age: 63
• Sex: Male
• Underwriting Class: Substandard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_63): 0.007232
• Underwriting Multiplier: 1.5x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 71% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $9112.73
• Expense Charge: $2278.18
• Reserve Accumulation: $3037.58
• Profit Margin: $759.39
• Gross Annual Premium: $15187.88

PAYMENT OPTIONS:
• Annual: $15187.88
• Semi-Annual: $7897.70 (x2 = $15795.39/year)
• Quarterly: $4024.79 (x4 = $16099.15/year)
• Monthly: $1366.91 (x12 = $16402.91/year)

RESERVE CALCULATIONS:
• Net Level Premium: $11390.91
• First Year Reserve: $3037.58
• Terminal Reserve (Year 2): $241789.52

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

Internal Rate of Return: 11.1%
Profit Margin: 9.4%
Lapse Assumption: 4.4% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Analyze mortality patterns for 1935 birth cohort

Response:
BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1935
Current Age: 89 years
Cohort Size at Birth: 2,397,703

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 71.3 years
• Current Life Expectancy: 75.3 years
• Survival to Current Age: 65.5%

HISTORICAL EXPOSURES:
• Standard exposures

MORTALITY PATTERN:
• Peak Infant Mortality: 24.1 per 1,000
• Current Mortality Rate: 9.1 per 1,000
• Improvement Since Birth: 36%

Cohort effects explain 29% of mortality variation.

Human: Analyze mortality patterns for 1935 birth cohort

Actuarial AI: BIRTH COHORT MORTALITY ANALYSIS

Birth Cohort: 1935
Current Age: 89 years
Cohort Size at Birth: 2,397,703

COHORT CHARACTERISTICS:
• Life Expectancy at Birth: 71.3 years
• Current Life Expectancy: 75.3 years
• Survival to Current Age: 65.5%

HISTORICAL EXPOSURES:
• Standard exposures

MORTALITY PATTERN:
• Peak Infant Mortality: 24.1 per 1,000
• Current Mortality Rate: 9.1 per 1,000
• Improvement Since Birth: 36%

Cohort effects explain 29% of mortality variation.


Instruction: Calculate excess mortality during seasonal flu in Brazil for 2022

Response:
EXCESS MORTALITY ANALYSIS

Event: seasonal flu
Location: Brazil
Period: 2022

MORTALITY METRICS:
• Expected Deaths (Baseline): 94,432
• Observed Deaths: 104,765
• Excess Deaths: 10,333
• Excess Mortality Rate: 10.9%
• P-score: 10.9%
• Z-score: 4.67 (p < 0.001)

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

AGE-SPECIFIC EXCESS:
• 0-44 years: 3.0% (1,033 deaths)
• 45-64 years: 18.5% (2,583 deaths)
• 65-74 years: 21.9% (2,583 deaths)
• 75+ years: 23.4% (4,133 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 8,236 (54%)
• Indirect (probable): 2,335 (25%)
• Collateral (delayed care): 1,068 (19%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [8,783, 11,882]
• Probability of chance: < 0.001
• Power: 0.96

Years of Life Lost: 151432
Economic Impact: $6.7 billion
Quality-Adjusted Life Years Lost: 108992

Human: Calculate excess mortality during seasonal flu in Brazil for 2022

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: seasonal flu
Location: Brazil
Period: 2022

MORTALITY METRICS:
• Expected Deaths (Baseline): 94,432
• Observed Deaths: 104,765
• Excess Deaths: 10,333
• Excess Mortality Rate: 10.9%
• P-score: 10.9%
• Z-score: 4.67 (p < 0.001)

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

AGE-SPECIFIC EXCESS:
• 0-44 years: 3.0% (1,033 deaths)
• 45-64 years: 18.5% (2,583 deaths)
• 65-74 years: 21.9% (2,583 deaths)
• 75+ years: 23.4% (4,133 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 8,236 (54%)
• Indirect (probable): 2,335 (25%)
• Collateral (delayed care): 1,068 (19%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [8,783, 11,882]
• Probability of chance: < 0.001
• Power: 0.96

Years of Life Lost: 151432
Economic Impact: $6.7 billion
Quality-Adjusted Life Years Lost: 108992


Instruction: Project mortality rates for UK in 2046

Response:
MORTALITY PROJECTION

Country: UK
Target Year: 2046
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 630.7 per 100,000
• Life Expectancy: 82.1 years
• Annual Improvement: 1.61%

CONFIDENCE INTERVALS (95%):
• Lower: 536.1
• Upper: 725.3

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

Human: Project mortality rates for UK in 2046

Actuarial AI: MORTALITY PROJECTION

Country: UK
Target Year: 2046
Projection Method: Lee-Carter Model with Coherent Forecasting

PROJECTED METRICS:
• Crude Death Rate: 630.7 per 100,000
• Life Expectancy: 82.1 years
• Annual Improvement: 1.61%

CONFIDENCE INTERVALS (95%):
• Lower: 536.1
• Upper: 725.3

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


Instruction: Analyze mortality differences by marital status in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

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

MORTALITY RATES BY MARITAL STATUS (per 100,000):
• Married: 337.2
• Single: 788.3
• Divorced: 658.0
• Widowed: 726.1

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.65
• Rate Difference: 612.9 per 100,000
• Population Attributable Risk: 33.5%
• Gini Coefficient: 0.132

LIFE EXPECTANCY BY MARITAL STATUS:
• Married: 72.9 years
• Single: 84.7 years
• Divorced: 83.1 years
• Widowed: 79.9 years

CONTRIBUTING FACTORS:
• Healthcare Access: 30% of disparity
• Socioeconomic Status: 24% of disparity
• Environmental Factors: 21% of disparity
• Behavioral Factors: 24% of disparity
• Biological Factors: 6% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: -1.7%

Social determinants explain 79% of observed mortality differences.

Human: Analyze mortality differences by marital status in the USA

Actuarial AI: DEMOGRAPHIC MORTALITY ANALYSIS

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

MORTALITY RATES BY MARITAL STATUS (per 100,000):
• Married: 337.2
• Single: 788.3
• Divorced: 658.0
• Widowed: 726.1

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.65
• Rate Difference: 612.9 per 100,000
• Population Attributable Risk: 33.5%
• Gini Coefficient: 0.132

LIFE EXPECTANCY BY MARITAL STATUS:
• Married: 72.9 years
• Single: 84.7 years
• Divorced: 83.1 years
• Widowed: 79.9 years

CONTRIBUTING FACTORS:
• Healthcare Access: 30% of disparity
• Socioeconomic Status: 24% of disparity
• Environmental Factors: 21% of disparity
• Behavioral Factors: 24% of disparity
• Biological Factors: 6% of disparity

TREND ANALYSIS:
• Disparities are narrowing
• Annual change in disparity: -1.7%

Social determinants explain 79% of observed mortality differences.


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

Response:
LIFE INSURANCE PREMIUM CALCULATION

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

PREMIUM COMPUTATION:
• Base Mortality Rate (q_41): 0.001541
• Underwriting Multiplier: 0.9x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 96% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $323.51
• Expense Charge: $80.88
• Reserve Accumulation: $107.84
• Profit Margin: $26.96
• Gross Annual Premium: $539.18

PAYMENT OPTIONS:
• Annual: $539.18
• Semi-Annual: $280.37 (x2 = $560.75/year)
• Quarterly: $142.88 (x4 = $571.53/year)
• Monthly: $48.53 (x12 = $582.32/year)

RESERVE CALCULATIONS:
• Net Level Premium: $404.39
• First Year Reserve: $107.84
• Terminal Reserve (Year 24): $48826.67

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

Internal Rate of Return: 11.0%
Profit Margin: 12.3%
Lapse Assumption: 4.2% annual

Illustration assumes guaranteed rates. Actual results may vary.

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

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

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

PREMIUM COMPUTATION:
• Base Mortality Rate (q_41): 0.001541
• Underwriting Multiplier: 0.9x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 96% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $323.51
• Expense Charge: $80.88
• Reserve Accumulation: $107.84
• Profit Margin: $26.96
• Gross Annual Premium: $539.18

PAYMENT OPTIONS:
• Annual: $539.18
• Semi-Annual: $280.37 (x2 = $560.75/year)
• Quarterly: $142.88 (x4 = $571.53/year)
• Monthly: $48.53 (x12 = $582.32/year)

RESERVE CALCULATIONS:
• Net Level Premium: $404.39
• First Year Reserve: $107.84
• Terminal Reserve (Year 24): $48826.67

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

Internal Rate of Return: 11.0%
Profit Margin: 12.3%
Lapse Assumption: 4.2% annual

Illustration assumes guaranteed rates. Actual results may vary.


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

Response:
OCCUPATIONAL MORTALITY ANALYSIS

Industry: Manufacturing
Fatal Injury Rate: 106.3 per 100,000 full-time workers
Annual Deaths: 10,443

LEADING CAUSES:
• Falls: 37%
• Struck by object: 28%
• Electrocution: 7%
• Caught-in/between: 16%

Workers' compensation death benefit: $448,698

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

Actuarial AI: OCCUPATIONAL MORTALITY ANALYSIS

Industry: Manufacturing
Fatal Injury Rate: 106.3 per 100,000 full-time workers
Annual Deaths: 10,443

LEADING CAUSES:
• Falls: 37%
• Struck by object: 28%
• Electrocution: 7%
• Caught-in/between: 16%

Workers' compensation death benefit: $448,698


Instruction: Compare cancer mortality between Canada, China and Australia

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Cancer Mortality
Countries: Canada, China, Australia
Reference Year: 2020

COMPARATIVE STATISTICS:
• Canada: 84.9 per 100,000 population
• China: 146.4 per 100,000 population
• Australia: 53.8 per 100,000 population

RANKINGS:
1. Australia: 53.8
2. Canada: 84.9
3. China: 146.4

STATISTICAL ANALYSIS:
• Range: 92.6
• Mean: 95.1
• Median: 84.9
• Standard Deviation: 38.5
• Coefficient of Variation: 40.5%

RELATIVE COMPARISONS:
• Best vs Worst: 2.72x difference
• Above Average: 1/3
• Global Ranking: Canada: #121, China: #63, Australia: #61

CONTRIBUTING FACTORS:
• Healthcare System: 29% of variation
• Economic Development: 27% of variation
• Public Health Policy: 18% of variation
• Demographics: 17% of variation
• Environmental Factors: 13% of variation

Convergence/Divergence: Diverging at 1.2% annually

Human: Compare cancer mortality between Canada, China and Australia

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Cancer Mortality
Countries: Canada, China, Australia
Reference Year: 2020

COMPARATIVE STATISTICS:
• Canada: 84.9 per 100,000 population
• China: 146.4 per 100,000 population
• Australia: 53.8 per 100,000 population

RANKINGS:
1. Australia: 53.8
2. Canada: 84.9
3. China: 146.4

STATISTICAL ANALYSIS:
• Range: 92.6
• Mean: 95.1
• Median: 84.9
• Standard Deviation: 38.5
• Coefficient of Variation: 40.5%

RELATIVE COMPARISONS:
• Best vs Worst: 2.72x difference
• Above Average: 1/3
• Global Ranking: Canada: #121, China: #63, Australia: #61

CONTRIBUTING FACTORS:
• Healthcare System: 29% of variation
• Economic Development: 27% of variation
• Public Health Policy: 18% of variation
• Demographics: 17% of variation
• Environmental Factors: 13% of variation

Convergence/Divergence: Diverging at 1.2% annually


Instruction: Summarize annuity mortality experience study results

Response:
MORTALITY EXPERIENCE STUDY

Study Type: Annuity Insurance
Study Period: 2021-2022
Exposure: 415880 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 1.10
• Deaths Actual: 8,455
• Deaths Expected: 5,387

BY DURATION:
• Select Period (Years 1-5): 0.71
• Ultimate (Years 6+): 0.99

Statistical confidence: 95% CI [0.90, 1.05]

Human: Summarize annuity mortality experience study results

Actuarial AI: MORTALITY EXPERIENCE STUDY

Study Type: Annuity Insurance
Study Period: 2021-2022
Exposure: 415880 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 1.10
• Deaths Actual: 8,455
• Deaths Expected: 5,387

BY DURATION:
• Select Period (Years 1-5): 0.71
• Ultimate (Years 6+): 0.99

Statistical confidence: 95% CI [0.90, 1.05]


Instruction: Compare suburban vs other area mortality rates in USA

Response:
GEOGRAPHIC MORTALITY ANALYSIS

Country: USA
Focus: Suburban Areas

MORTALITY RATES (per 100,000):
• Urban: 770.2
• Rural: 984.6
• Suburban: 700.1

Rural areas show 27.8% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.

Human: Compare suburban vs other area mortality rates in USA

Actuarial AI: GEOGRAPHIC MORTALITY ANALYSIS

Country: USA
Focus: Suburban Areas

MORTALITY RATES (per 100,000):
• Urban: 770.2
• Rural: 984.6
• Suburban: 700.1

Rural areas show 27.8% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.


Instruction: What is the life expectancy for a 20 year old female in India as of 2016?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: India
• Age: 20 years
• Sex: Female
• Reference Year: 2016

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 20 (e_20): 50.6 years
• Expected Age at Death: 70.6 years
• Median Survival Time: 35.1 years
• Modal Age at Death: 65.6 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_20): 90.8%
• 10-Year Survival (₁₀p_20): 82.4%
• 20-Year Survival (₂₀p_20): 67.9%

MORTALITY METRICS:
• Force of Mortality (μ_20): 0.01939
• Probability of Death within 1 Year (q_20): 0.01920
• Hazard Rate: 0.01958

COMPARATIVE CONTEXT:
• Global Average at Age 20: 49.7 years
• Regional Rank: Top 32 globally
• Historical Trend: Improving

Based on 154,769 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 5.0%.

Human: What is the life expectancy for a 20 year old female in India as of 2016?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: India
• Age: 20 years
• Sex: Female
• Reference Year: 2016

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 20 (e_20): 50.6 years
• Expected Age at Death: 70.6 years
• Median Survival Time: 35.1 years
• Modal Age at Death: 65.6 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_20): 90.8%
• 10-Year Survival (₁₀p_20): 82.4%
• 20-Year Survival (₂₀p_20): 67.9%

MORTALITY METRICS:
• Force of Mortality (μ_20): 0.01939
• Probability of Death within 1 Year (q_20): 0.01920
• Hazard Rate: 0.01958

COMPARATIVE CONTEXT:
• Global Average at Age 20: 49.7 years
• Regional Rank: Top 32 globally
• Historical Trend: Improving

Based on 154,769 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 5.0%.


Instruction: Analyze mortality impact of COVID-19

Response:
PANDEMIC MORTALITY ANALYSIS

Pandemic: COVID-19
Global Deaths: 6,887,285
Case Fatality Rate: 5.6%
Infection Fatality Rate: 0.25%

Age-specific mortality shows exponential increase with age.
Economic impact: $8.9 trillion globally.

Human: Analyze mortality impact of COVID-19

Actuarial AI: PANDEMIC MORTALITY ANALYSIS

Pandemic: COVID-19
Global Deaths: 6,887,285
Case Fatality Rate: 5.6%
Infection Fatality Rate: 0.25%

Age-specific mortality shows exponential increase with age.
Economic impact: $8.9 trillion globally.


Instruction: Compare cardiovascular mortality between Brazil, Mexico, India and France

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Cardiovascular Mortality
Countries: Brazil, Mexico, India, France
Reference Year: 2023

COMPARATIVE STATISTICS:
• Brazil: 197.6 per 100,000 population
• Mexico: 56.2 per 100,000 population
• India: 73.5 per 100,000 population
• France: 180.8 per 100,000 population

RANKINGS:
1. Mexico: 56.2
2. India: 73.5
3. France: 180.8
4. Brazil: 197.6

STATISTICAL ANALYSIS:
• Range: 141.4
• Mean: 127.0
• Median: 127.2
• Standard Deviation: 62.8
• Coefficient of Variation: 49.4%

RELATIVE COMPARISONS:
• Best vs Worst: 3.52x difference
• Above Average: 2/4
• Global Ranking: Brazil: #157, Mexico: #66, India: #68

CONTRIBUTING FACTORS:
• Healthcare System: 39% of variation
• Economic Development: 35% of variation
• Public Health Policy: 23% of variation
• Demographics: 13% of variation
• Environmental Factors: 7% of variation

Convergence/Divergence: Converging at 1.0% annually

Human: Compare cardiovascular mortality between Brazil, Mexico, India and France

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Cardiovascular Mortality
Countries: Brazil, Mexico, India, France
Reference Year: 2023

COMPARATIVE STATISTICS:
• Brazil: 197.6 per 100,000 population
• Mexico: 56.2 per 100,000 population
• India: 73.5 per 100,000 population
• France: 180.8 per 100,000 population

RANKINGS:
1. Mexico: 56.2
2. India: 73.5
3. France: 180.8
4. Brazil: 197.6

STATISTICAL ANALYSIS:
• Range: 141.4
• Mean: 127.0
• Median: 127.2
• Standard Deviation: 62.8
• Coefficient of Variation: 49.4%

RELATIVE COMPARISONS:
• Best vs Worst: 3.52x difference
• Above Average: 2/4
• Global Ranking: Brazil: #157, Mexico: #66, India: #68

CONTRIBUTING FACTORS:
• Healthcare System: 39% of variation
• Economic Development: 35% of variation
• Public Health Policy: 23% of variation
• Demographics: 13% of variation
• Environmental Factors: 7% of variation

Convergence/Divergence: Converging at 1.0% annually