Instruction: What is the unhedged proﬁt of MBF?

Response: 75 RISK MANAGEMENT 641 Figure 75.3 The proﬁt per pound that results from selling the 3.4-strike call is P1 −3 −max{P1 −3.4,0}+ 0.3762e0.05. The graph of the proﬁt is given in Figure 75.3. (e) The proﬁt is S1 −3 + max{3.6 −S1,0}−max{3.4 −S1,0}−(0.3856 −0.19196)e0.05. Under this strategy the proﬁt of the company is very close to that of a forward contract. But, instead of winning a constant of $0.5/lb. in the forward contract, the company’s proﬁt varies with the future price of copper, although not much The Buyer’s Perspective A buyer of the producer’s product is in the opposite position from the producer. The buyer can engage in any of the above risk management strategies, but would do the opposite of what the producer does. The buyer’s possible strategies are therefore as follows: •Enter into a long forward contract. •Sell a put option (ﬂoor). •Buy a call option (cap). Example 75.2 MBF is a wire manufacturer. It buys copper and manufactures wires. Suppose the ﬁxed cost of a unit of wire is $2 and the noncopper variable cost is $1.25. A unit of wire sells for $5 plus the price of copper. One pound of copper is needed to manufacture one unit of wire. (a) (b) Suppose that MBF buys a forward contract with forward price of $3.5/lb. What is the proﬁt one year from now? Solution. (a) MBF needs copper to manufacture its product. Thus, an increase in copper price results in an increase in cost of making the wire. So one may think that the company needs to hedge for the price ﬂuctuations. But since the company will adjust its selling price to reﬂect the change in the copper price, this chnage will cancel the copper price risk and as a result there is no need for hedging. The unhedged proﬁt per pound of copper in one year from today is Revenue −Cost = P1 + 5 −(2 + 1.25 + P1) = 1.75. 642 AN INTRODUCTION TO THE MATHEMATICS OF FINANCIAL DERIVATIVES We see that the proﬁts of MBF do not depend on the price of copper. Cost and revenue copper price risk cancel each other out. (b) In this case, the proﬁt per pound of copper one year from today is given by P1 + 5 −(2 + 1.25 + P1) + P1 −3.5 = P1 −1.75. Note that buying a forward introduces price risk Example 75.3 Alumco is a company that manufactures dishwashers. It uses aluminum to make their product. Each dishwasher requires 5 pounds of aluminum. The ﬁxed cost is $100 and the selling price is $350. (a) What is the unhedged proﬁt one year from now? (b) Alumco could faces severe loses if the price of the aluminum goes very high. To hedge risk, the company buys forward contract with the current forward price of $40 per pound. What is the proﬁt one year from now per dishwasher? (c) Another alternative to hedge the aluminum price risk is to buy a call. Suppose that Alumco buys a 35-strike call with an expiration date one year from now, nominal amount 5 lbs, and for a premium of $7.609104. The one year continuously compounded interest rate is 6%. Find the proﬁt one year from now per dishwasher. (d) Another alternative to hedge the aluminum price risk is to sell a put. Suppose that Alumco sells a 35-strike put with an expiration date one year from now, nominal amount 5 lbs, and for a premium of $7.609104. Find the proﬁt one year from now per dishwasher. Solution. (a) Let P1 be the price of one pound of aluminum one year from now. The proﬁt from selling one dishwasher one year from now is given by 350 −(5P1 + 100) = 250 −5P1. The unisured proﬁt is shown in Figure 75.4. (b) The proﬁt of entering a long forward is 350 −(5 ×40 + 100) = $50. The graph of this proﬁt is shown in Figure 75.4. (c) The proﬁt that results from buying the call is 250 −5S1 + 5 max{S1 −35,0}−5(7.609104)e0.06 = 209.602 −5S1 + 5 max{S1 −35,0}. 75 RISK MANAGEMENT 643 The graph of the proﬁt is shown in Figure 75.4. (d) The proﬁt that results from selling the put is 250 −5S1 −5 max{35 −S1,0}+ 5(7.609104)e0.06 = 290.40 −5S1 −5 max{35 −S1,0} Figure 75.4 Why do ﬁrms manage risks through derivatives? Firms engage in hedging for a variety of reasons namely: •To lower expected taxes •To lower ﬁnancial distress costs:A large loss can threaten the survival of a ﬁrm. For example, a money-losing ﬁrm may be unable to meet ﬁxed obligations (such as, debt payments and wages). If a ﬁrm appears in ﬁnancial distress, customers may be less willing to purchase its goods (for the fear that the ﬁrm may go out of business and therefore will not provide warranty for its goods). A ﬁrm uses derivatives to transfer income from proﬁt states to loss states. Hedging allows a ﬁrm to reduce the probability of bankruptcy or ﬁnancial distress. •To lower costly external ﬁnance: Usually when a form is in a loss state they have to oﬀset that by either using cash reserve or raising funds (by borrowing or issuing bonds). Borrowing entails costs such as underwriting fees and high interest rates (because the lender fears for his money when the borrower is in s loss state). If a ﬁrm uses its cash reserve to pay for the losses, this reduction in cash can increase the probability of costly external ﬁnancing and can lead a ﬁrm to forego invest- ment projects it would have taken had cash been available to use for ﬁnancing. Thus, hedging with derivatives can safeguard cash reserves and reduce the probability of raising funds externally. •Increasing debt capacity: That is the amount a company can borrow. •Managerial risk aversion: Firm managers are typically not well-diversiﬁed. Salary, bonus, 644 AN INTRODUCTION TO THE MATHEMATICS OF FINANCIAL DERIVATIVES and compensation are tied to the performance of the ﬁrm. Poor diversiﬁcation makes managers risk-averse, i.e., they are harmed by a dollar of loss more than they are helped by a dollar of gain. Managers have incentives to reduce uncertainty through hedging. As there are reasons for hedging, there are also reasons why a company may choose not to hedge, namely: •Transaction costs of engaging in hedges (such as commissions and the bid-ask spread) •The cost of expertise required to analyze a hedging strategy •The cost of monitoring and controlling the hedging transactions. •Potential collateral requirements associated with some types of hedging. •The tax and accounting consequences of hedges. In the real world, small companies are discouraged to do derivatives because the reasons above. However, large companies have ﬁnancial, accounting and legal departments which allow them to take advantage of the opportunities on market derivatives. The ﬁnancial department of a large company can asses derivatives as well or better than the market does. Their legal and accounting departments allow them to take advantage of the current tax laws. Answer Key The answer key to the book can be requested directly from the author through email: mﬁ- nan@atu.edu 645 646 ANSWER KEY Bibliography [1] S. Kellison , The Theory of Interest , 2nd Edition (1991), McGraw-Hill. [2] R.L. McDonald , Derivatives Markets, 2nd Edition (2006), Pearson. [3] SOA/CAS, Exam FM Sample Questions. 647

Human: What is the unhedged proﬁt of MBF?

Actuarial AI: 75 RISK MANAGEMENT 641 Figure 75.3 The proﬁt per pound that results from selling the 3.4-strike call is P1 −3 −max{P1 −3.4,0}+ 0.3762e0.05. The graph of the proﬁt is given in Figure 75.3. (e) The proﬁt is S1 −3 + max{3.6 −S1,0}−max{3.4 −S1,0}−(0.3856 −0.19196)e0.05. Under this strategy the proﬁt of the company is very close to that of a forward contract. But, instead of winning a constant of $0.5/lb. in the forward contract, the company’s proﬁt varies with the future price of copper, although not much The Buyer’s Perspective A buyer of the producer’s product is in the opposite position from the producer. The buyer can engage in any of the above risk management strategies, but would do the opposite of what the producer does. The buyer’s possible strategies are therefore as follows: •Enter into a long forward contract. •Sell a put option (ﬂoor). •Buy a call option (cap). Example 75.2 MBF is a wire manufacturer. It buys copper and manufactures wires. Suppose the ﬁxed cost of a unit of wire is $2 and the noncopper variable cost is $1.25. A unit of wire sells for $5 plus the price of copper. One pound of copper is needed to manufacture one unit of wire. (a) (b) Suppose that MBF buys a forward contract with forward price of $3.5/lb. What is the proﬁt one year from now? Solution. (a) MBF needs copper to manufacture its product. Thus, an increase in copper price results in an increase in cost of making the wire. So one may think that the company needs to hedge for the price ﬂuctuations. But since the company will adjust its selling price to reﬂect the change in the copper price, this chnage will cancel the copper price risk and as a result there is no need for hedging. The unhedged proﬁt per pound of copper in one year from today is Revenue −Cost = P1 + 5 −(2 + 1.25 + P1) = 1.75. 642 AN INTRODUCTION TO THE MATHEMATICS OF FINANCIAL DERIVATIVES We see that the proﬁts of MBF do not depend on the price of copper. Cost and revenue copper price risk cancel each other out. (b) In this case, the proﬁt per pound of copper one year from today is given by P1 + 5 −(2 + 1.25 + P1) + P1 −3.5 = P1 −1.75. Note that buying a forward introduces price risk Example 75.3 Alumco is a company that manufactures dishwashers. It uses aluminum to make their product. Each dishwasher requires 5 pounds of aluminum. The ﬁxed cost is $100 and the selling price is $350. (a) What is the unhedged proﬁt one year from now? (b) Alumco could faces severe loses if the price of the aluminum goes very high. To hedge risk, the company buys forward contract with the current forward price of $40 per pound. What is the proﬁt one year from now per dishwasher? (c) Another alternative to hedge the aluminum price risk is to buy a call. Suppose that Alumco buys a 35-strike call with an expiration date one year from now, nominal amount 5 lbs, and for a premium of $7.609104. The one year continuously compounded interest rate is 6%. Find the proﬁt one year from now per dishwasher. (d) Another alternative to hedge the aluminum price risk is to sell a put. Suppose that Alumco sells a 35-strike put with an expiration date one year from now, nominal amount 5 lbs, and for a premium of $7.609104. Find the proﬁt one year from now per dishwasher. Solution. (a) Let P1 be the price of one pound of aluminum one year from now. The proﬁt from selling one dishwasher one year from now is given by 350 −(5P1 + 100) = 250 −5P1. The unisured proﬁt is shown in Figure 75.4. (b) The proﬁt of entering a long forward is 350 −(5 ×40 + 100) = $50. The graph of this proﬁt is shown in Figure 75.4. (c) The proﬁt that results from buying the call is 250 −5S1 + 5 max{S1 −35,0}−5(7.609104)e0.06 = 209.602 −5S1 + 5 max{S1 −35,0}. 75 RISK MANAGEMENT 643 The graph of the proﬁt is shown in Figure 75.4. (d) The proﬁt that results from selling the put is 250 −5S1 −5 max{35 −S1,0}+ 5(7.609104)e0.06 = 290.40 −5S1 −5 max{35 −S1,0} Figure 75.4 Why do ﬁrms manage risks through derivatives? Firms engage in hedging for a variety of reasons namely: •To lower expected taxes •To lower ﬁnancial distress costs:A large loss can threaten the survival of a ﬁrm. For example, a money-losing ﬁrm may be unable to meet ﬁxed obligations (such as, debt payments and wages). If a ﬁrm appears in ﬁnancial distress, customers may be less willing to purchase its goods (for the fear that the ﬁrm may go out of business and therefore will not provide warranty for its goods). A ﬁrm uses derivatives to transfer income from proﬁt states to loss states. Hedging allows a ﬁrm to reduce the probability of bankruptcy or ﬁnancial distress. •To lower costly external ﬁnance: Usually when a form is in a loss state they have to oﬀset that by either using cash reserve or raising funds (by borrowing or issuing bonds). Borrowing entails costs such as underwriting fees and high interest rates (because the lender fears for his money when the borrower is in s loss state). If a ﬁrm uses its cash reserve to pay for the losses, this reduction in cash can increase the probability of costly external ﬁnancing and can lead a ﬁrm to forego invest- ment projects it would have taken had cash been available to use for ﬁnancing. Thus, hedging with derivatives can safeguard cash reserves and reduce the probability of raising funds externally. •Increasing debt capacity: That is the amount a company can borrow. •Managerial risk aversion: Firm managers are typically not well-diversiﬁed. Salary, bonus, 644 AN INTRODUCTION TO THE MATHEMATICS OF FINANCIAL DERIVATIVES and compensation are tied to the performance of the ﬁrm. Poor diversiﬁcation makes managers risk-averse, i.e., they are harmed by a dollar of loss more than they are helped by a dollar of gain. Managers have incentives to reduce uncertainty through hedging. As there are reasons for hedging, there are also reasons why a company may choose not to hedge, namely: •Transaction costs of engaging in hedges (such as commissions and the bid-ask spread) •The cost of expertise required to analyze a hedging strategy •The cost of monitoring and controlling the hedging transactions. •Potential collateral requirements associated with some types of hedging. •The tax and accounting consequences of hedges. In the real world, small companies are discouraged to do derivatives because the reasons above. However, large companies have ﬁnancial, accounting and legal departments which allow them to take advantage of the opportunities on market derivatives. The ﬁnancial department of a large company can asses derivatives as well or better than the market does. Their legal and accounting departments allow them to take advantage of the current tax laws. Answer Key The answer key to the book can be requested directly from the author through email: mﬁ- nan@atu.edu 645 646 ANSWER KEY Bibliography [1] S. Kellison , The Theory of Interest , 2nd Edition (1991), McGraw-Hill. [2] R.L. McDonald , Derivatives Markets, 2nd Edition (2006), Pearson. [3] SOA/CAS, Exam FM Sample Questions. 647


Instruction: What is the life expectancy for a 42 year old male in Australia as of 2017?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Australia
• Age: 42 years
• Sex: Male
• Reference Year: 2017

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 42 (e_42): 37.4 years
• Expected Age at Death: 79.4 years
• Median Survival Time: 25.9 years
• Modal Age at Death: 74.4 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_42): 87.8%
• 10-Year Survival (₁₀p_42): 77.1%
• 20-Year Survival (₂₀p_42): 59.4%

MORTALITY METRICS:
• Force of Mortality (μ_42): 0.02601
• Probability of Death within 1 Year (q_42): 0.02568
• Hazard Rate: 0.02636

COMPARATIVE CONTEXT:
• Global Average at Age 42: 40.9 years
• Regional Rank: Top 13 globally
• Historical Trend: Improving

Based on 145,037 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.7%.

Human: What is the life expectancy for a 42 year old male in Australia as of 2017?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Australia
• Age: 42 years
• Sex: Male
• Reference Year: 2017

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 42 (e_42): 37.4 years
• Expected Age at Death: 79.4 years
• Median Survival Time: 25.9 years
• Modal Age at Death: 74.4 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_42): 87.8%
• 10-Year Survival (₁₀p_42): 77.1%
• 20-Year Survival (₂₀p_42): 59.4%

MORTALITY METRICS:
• Force of Mortality (μ_42): 0.02601
• Probability of Death within 1 Year (q_42): 0.02568
• Hazard Rate: 0.02636

COMPARATIVE CONTEXT:
• Global Average at Age 42: 40.9 years
• Regional Rank: Top 13 globally
• Historical Trend: Improving

Based on 145,037 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 2.7%.


Instruction: What is the mortality rate for Chronic Respiratory in France for 75+ in 2019?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Chronic Respiratory
Location: France
Year: 2019
Age Group: 75+

MORTALITY STATISTICS:
• Crude Death Rate: 32.2 per 100,000 population
• Age-Adjusted Rate: 29.7 per 100,000
• Total Deaths: 148,196
• Percentage of All Deaths: 5.6%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 38.6 per 100,000
• Female Death Rate: 27.3 per 100,000
• Sex Ratio (M:F): 1.41:1

TREND ANALYSIS:
• 5-Year Change: +11.7%
• 10-Year Change: -17.2%
• Annual Percentage Change: +1.7%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #9
• Years of Potential Life Lost (YPLL): 3558948
• Economic Burden: $90.7 billion annually
• Preventable Deaths: 32%

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

International Classification of Diseases (ICD-10): J40-J47
Data Quality: Near-Complete (88% coverage)

Human: What is the mortality rate for Chronic Respiratory in France for 75+ in 2019?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Chronic Respiratory
Location: France
Year: 2019
Age Group: 75+

MORTALITY STATISTICS:
• Crude Death Rate: 32.2 per 100,000 population
• Age-Adjusted Rate: 29.7 per 100,000
• Total Deaths: 148,196
• Percentage of All Deaths: 5.6%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 38.6 per 100,000
• Female Death Rate: 27.3 per 100,000
• Sex Ratio (M:F): 1.41:1

TREND ANALYSIS:
• 5-Year Change: +11.7%
• 10-Year Change: -17.2%
• Annual Percentage Change: +1.7%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #9
• Years of Potential Life Lost (YPLL): 3558948
• Economic Burden: $90.7 billion annually
• Preventable Deaths: 32%

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

International Classification of Diseases (ICD-10): J40-J47
Data Quality: Near-Complete (88% coverage)


Instruction: Calculate Term life insurance premium for 58 year old female, $5,000,000 coverage, 25 year term, Standard Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $5,000,000
• Term Length: 25 years
• Issue Age: 58
• Sex: Female
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_58): 0.002715
• Underwriting Multiplier: 0.9x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 100% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $8144.96
• Expense Charge: $2036.24
• Reserve Accumulation: $2714.99
• Profit Margin: $678.75
• Gross Annual Premium: $13574.94

PAYMENT OPTIONS:
• Annual: $13574.94
• Semi-Annual: $7058.97 (x2 = $14117.93/year)
• Quarterly: $3597.36 (x4 = $14389.43/year)
• Monthly: $1221.74 (x12 = $14660.93/year)

RESERVE CALCULATIONS:
• Net Level Premium: $10181.20
• First Year Reserve: $2714.99
• Terminal Reserve (Year 25): $2178071.13

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

Internal Rate of Return: 10.4%
Profit Margin: 10.9%
Lapse Assumption: 7.1% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Term life insurance premium for 58 year old female, $5,000,000 coverage, 25 year term, Standard Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $5,000,000
• Term Length: 25 years
• Issue Age: 58
• Sex: Female
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_58): 0.002715
• Underwriting Multiplier: 0.9x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 100% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $8144.96
• Expense Charge: $2036.24
• Reserve Accumulation: $2714.99
• Profit Margin: $678.75
• Gross Annual Premium: $13574.94

PAYMENT OPTIONS:
• Annual: $13574.94
• Semi-Annual: $7058.97 (x2 = $14117.93/year)
• Quarterly: $3597.36 (x4 = $14389.43/year)
• Monthly: $1221.74 (x12 = $14660.93/year)

RESERVE CALCULATIONS:
• Net Level Premium: $10181.20
• First Year Reserve: $2714.99
• Terminal Reserve (Year 25): $2178071.13

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

Internal Rate of Return: 10.4%
Profit Margin: 10.9%
Lapse Assumption: 7.1% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Perform mortality assumption review for life insurance portfolio

Response:
MORTALITY ASSUMPTION VALUATION

Product: Life Insurance Portfolio
Valuation Date: 12/31/2024

CURRENT ASSUMPTIONS:
• Base Table: RP-2014
• Improvement Scale: MP-2020
• Experience Adjustment: 90%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 0.95
• Credibility Factor: 0.90
• Indicated Change: -5.8%

FINANCIAL IMPACT:
• Reserve Change: $-3.7 million
• Funded Ratio Impact: +1.7%

Recommendation: Maintain current assumptions

Human: Perform mortality assumption review for life insurance portfolio

Actuarial AI: MORTALITY ASSUMPTION VALUATION

Product: Life Insurance Portfolio
Valuation Date: 12/31/2024

CURRENT ASSUMPTIONS:
• Base Table: RP-2014
• Improvement Scale: MP-2020
• Experience Adjustment: 90%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 0.95
• Credibility Factor: 0.90
• Indicated Change: -5.8%

FINANCIAL IMPACT:
• Reserve Change: $-3.7 million
• Funded Ratio Impact: +1.7%

Recommendation: Maintain current assumptions


Instruction: What is the mortality rate for COVID-19 in UK for 25-44 in 2021?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: COVID-19
Location: UK
Year: 2021
Age Group: 25-44

MORTALITY STATISTICS:
• Crude Death Rate: 81.3 per 100,000 population
• Age-Adjusted Rate: 69.1 per 100,000
• Total Deaths: 1,608,694
• Percentage of All Deaths: 19.5%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 97.5 per 100,000
• Female Death Rate: 69.1 per 100,000
• Sex Ratio (M:F): 1.22:1

TREND ANALYSIS:
• 5-Year Change: +14.4%
• 10-Year Change: -16.0%
• Annual Percentage Change: +2.4%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #3
• Years of Potential Life Lost (YPLL): 22388500
• Economic Burden: $63.6 billion annually
• Preventable Deaths: 24%

RISK FACTORS:
• Age > 65: 80% of deaths
• Comorbidities: 75%
• Obesity: 30%
• Diabetes: 40%
• Immunocompromised: 20%

International Classification of Diseases (ICD-10): U07.1
Data Quality: Near-Complete (97% coverage)

Human: What is the mortality rate for COVID-19 in UK for 25-44 in 2021?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: COVID-19
Location: UK
Year: 2021
Age Group: 25-44

MORTALITY STATISTICS:
• Crude Death Rate: 81.3 per 100,000 population
• Age-Adjusted Rate: 69.1 per 100,000
• Total Deaths: 1,608,694
• Percentage of All Deaths: 19.5%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 97.5 per 100,000
• Female Death Rate: 69.1 per 100,000
• Sex Ratio (M:F): 1.22:1

TREND ANALYSIS:
• 5-Year Change: +14.4%
• 10-Year Change: -16.0%
• Annual Percentage Change: +2.4%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #3
• Years of Potential Life Lost (YPLL): 22388500
• Economic Burden: $63.6 billion annually
• Preventable Deaths: 24%

RISK FACTORS:
• Age > 65: 80% of deaths
• Comorbidities: 75%
• Obesity: 30%
• Diabetes: 40%
• Immunocompromised: 20%

International Classification of Diseases (ICD-10): U07.1
Data Quality: Near-Complete (97% coverage)


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

Response:
EXCESS MORTALITY ANALYSIS

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

MORTALITY METRICS:
• Expected Deaths (Baseline): 90,596
• Observed Deaths: 100,784
• Excess Deaths: 10,188
• Excess Mortality Rate: 11.2%
• P-score: 11.2%
• Z-score: 4.39 (p < 0.001)

BASELINE CALCULATION:
• Method: Farrington surveillance
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.5% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: -2.9% (1,018 deaths)
• 45-64 years: 8.9% (2,547 deaths)
• 65-74 years: 22.1% (2,547 deaths)
• 75+ years: 39.3% (4,075 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 7,150 (71%)
• Indirect (probable): 2,737 (23%)
• Collateral (delayed care): 1,410 (14%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [8,659, 11,716]
• Probability of chance: < 0.001
• Power: 0.97

Years of Life Lost: 141569
Economic Impact: $1.7 billion
Quality-Adjusted Life Years Lost: 93033

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

Actuarial AI: EXCESS MORTALITY ANALYSIS

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

MORTALITY METRICS:
• Expected Deaths (Baseline): 90,596
• Observed Deaths: 100,784
• Excess Deaths: 10,188
• Excess Mortality Rate: 11.2%
• P-score: 11.2%
• Z-score: 4.39 (p < 0.001)

BASELINE CALCULATION:
• Method: Farrington surveillance
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.5% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: -2.9% (1,018 deaths)
• 45-64 years: 8.9% (2,547 deaths)
• 65-74 years: 22.1% (2,547 deaths)
• 75+ years: 39.3% (4,075 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 7,150 (71%)
• Indirect (probable): 2,737 (23%)
• Collateral (delayed care): 1,410 (14%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [8,659, 11,716]
• Probability of chance: < 0.001
• Power: 0.97

Years of Life Lost: 141569
Economic Impact: $1.7 billion
Quality-Adjusted Life Years Lost: 93033


Instruction: Show survival curve for Germany female in 2023

Response:
SURVIVAL CURVE ANALYSIS

Population: Germany Female
Reference Year: 2023
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         75.7
    1          99,998           10         0.00010         80.1
    5          99,988           21         0.00021         78.9
   10          99,967           63         0.00063         72.6
   20          99,904           97         0.00097         61.0
   30          99,807          182         0.00182         51.6
   40          99,625          339         0.00340         36.1
   50          99,286          428         0.00431         30.8
   60          98,858          707         0.00715         18.5
   70          98,151          984         0.01003         12.9
   80          97,167        1,304         0.01342          0.0
   90          95,863        1,607         0.01676          1.9
  100          94,256        2,746         0.02913          4.1
  110          91,510       91,510         1.00000          2.7

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: 98.9%
• Probability of Surviving to 80: 97.2%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 284,073 death certificates.

Human: Show survival curve for Germany female in 2023

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Germany Female
Reference Year: 2023
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         75.7
    1          99,998           10         0.00010         80.1
    5          99,988           21         0.00021         78.9
   10          99,967           63         0.00063         72.6
   20          99,904           97         0.00097         61.0
   30          99,807          182         0.00182         51.6
   40          99,625          339         0.00340         36.1
   50          99,286          428         0.00431         30.8
   60          98,858          707         0.00715         18.5
   70          98,151          984         0.01003         12.9
   80          97,167        1,304         0.01342          0.0
   90          95,863        1,607         0.01676          1.9
  100          94,256        2,746         0.02913          4.1
  110          91,510       91,510         1.00000          2.7

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: 98.9%
• Probability of Surviving to 80: 97.2%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 284,073 death certificates.


Instruction: What is the life expectancy for a 73 year old both in Australia as of 2018?

Response:
ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Australia
• Age: 73 years
• Sex: Both
• Reference Year: 2018

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 73 (e_73): 9.5 years
• Expected Age at Death: 82.5 years
• Median Survival Time: 6.6 years
• Modal Age at Death: 77.5 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_73): 62.2%
• 10-Year Survival (₁₀p_73): 38.7%
• 20-Year Survival (₂₀p_73): 14.9%

MORTALITY METRICS:
• Force of Mortality (μ_73): 0.09506
• Probability of Death within 1 Year (q_73): 0.09068
• Hazard Rate: 0.09989

COMPARATIVE CONTEXT:
• Global Average at Age 73: 9.9 years
• Regional Rank: Top 35 globally
• Historical Trend: Improving

Based on 114,304 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.6%.

Human: What is the life expectancy for a 73 year old both in Australia as of 2018?

Actuarial AI: ACTUARIAL ANALYSIS: Life Expectancy Calculation

Demographics:
• Location: Australia
• Age: 73 years
• Sex: Both
• Reference Year: 2018

LIFE EXPECTANCY METRICS:
• Life Expectancy at Age 73 (e_73): 9.5 years
• Expected Age at Death: 82.5 years
• Median Survival Time: 6.6 years
• Modal Age at Death: 77.5 years

SURVIVAL PROBABILITIES:
• 5-Year Survival (₅p_73): 62.2%
• 10-Year Survival (₁₀p_73): 38.7%
• 20-Year Survival (₂₀p_73): 14.9%

MORTALITY METRICS:
• Force of Mortality (μ_73): 0.09506
• Probability of Death within 1 Year (q_73): 0.09068
• Hazard Rate: 0.09989

COMPARATIVE CONTEXT:
• Global Average at Age 73: 9.9 years
• Regional Rank: Top 35 globally
• Historical Trend: Improving

Based on 114,304 death records and actuarial projections.
Each year survived reduces remaining uncertainty by 4.6%.


Instruction: What is the mortality rate for Chronic Respiratory in Germany for 75+ in 2024?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Chronic Respiratory
Location: Germany
Year: 2024
Age Group: 75+

MORTALITY STATISTICS:
• Crude Death Rate: 48.3 per 100,000 population
• Age-Adjusted Rate: 44.9 per 100,000
• Total Deaths: 2,252,914
• Percentage of All Deaths: 4.2%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 57.9 per 100,000
• Female Death Rate: 41.0 per 100,000
• Sex Ratio (M:F): 1.30:1

TREND ANALYSIS:
• 5-Year Change: -2.6%
• 10-Year Change: -22.3%
• Annual Percentage Change: +2.8%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #7
• Years of Potential Life Lost (YPLL): 31479107
• Economic Burden: $10.3 billion annually
• Preventable Deaths: 50%

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

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

Human: What is the mortality rate for Chronic Respiratory in Germany for 75+ in 2024?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Chronic Respiratory
Location: Germany
Year: 2024
Age Group: 75+

MORTALITY STATISTICS:
• Crude Death Rate: 48.3 per 100,000 population
• Age-Adjusted Rate: 44.9 per 100,000
• Total Deaths: 2,252,914
• Percentage of All Deaths: 4.2%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 57.9 per 100,000
• Female Death Rate: 41.0 per 100,000
• Sex Ratio (M:F): 1.30:1

TREND ANALYSIS:
• 5-Year Change: -2.6%
• 10-Year Change: -22.3%
• Annual Percentage Change: +2.8%
• Trend: Decreasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #7
• Years of Potential Life Lost (YPLL): 31479107
• Economic Burden: $10.3 billion annually
• Preventable Deaths: 50%

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

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


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

Response:
OCCUPATIONAL MORTALITY ANALYSIS

Industry: Agriculture
Fatal Injury Rate: 20.2 per 100,000 full-time workers
Annual Deaths: 1,329

LEADING CAUSES:
• Falls: 28%
• Struck by object: 19%
• Electrocution: 9%
• Caught-in/between: 11%

Workers' compensation death benefit: $383,133

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

Actuarial AI: OCCUPATIONAL MORTALITY ANALYSIS

Industry: Agriculture
Fatal Injury Rate: 20.2 per 100,000 full-time workers
Annual Deaths: 1,329

LEADING CAUSES:
• Falls: 28%
• Struck by object: 19%
• Electrocution: 9%
• Caught-in/between: 11%

Workers' compensation death benefit: $383,133


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: 841.8
• Rural: 932.3
• Suburban: 773.6

Rural areas show 10.8% 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: 841.8
• Rural: 932.3
• Suburban: 773.6

Rural areas show 10.8% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.


Instruction: Show survival curve for Brazil male in 2016

Response:
SURVIVAL CURVE ANALYSIS

Population: Brazil 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         75.3
    1          99,997           12         0.00012         82.8
    5          99,985           29         0.00029         78.0
   10          99,956           82         0.00082         65.5
   20          99,874          168         0.00168         58.9
   30          99,706          210         0.00211         49.5
   40          99,496          366         0.00368         41.7
   50          99,130          612         0.00617         33.7
   60          98,518          800         0.00812         24.4
   70          97,718        1,157         0.01184          5.2
   80          96,561        2,198         0.02276          2.2
   90          94,363        2,560         0.02713          2.4
  100          91,803        3,580         0.03900          1.9
  110          88,223       88,223         1.00000          2.1

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 81.2 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.5%
• Probability of Surviving to 80: 96.6%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.85

The survival curve follows Gompertz law after age 30.
Data sourced from 183,254 death certificates.

Human: Show survival curve for Brazil male in 2016

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Brazil 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         75.3
    1          99,997           12         0.00012         82.8
    5          99,985           29         0.00029         78.0
   10          99,956           82         0.00082         65.5
   20          99,874          168         0.00168         58.9
   30          99,706          210         0.00211         49.5
   40          99,496          366         0.00368         41.7
   50          99,130          612         0.00617         33.7
   60          98,518          800         0.00812         24.4
   70          97,718        1,157         0.01184          5.2
   80          96,561        2,198         0.02276          2.2
   90          94,363        2,560         0.02713          2.4
  100          91,803        3,580         0.03900          1.9
  110          88,223       88,223         1.00000          2.1

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 81.2 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.5%
• Probability of Surviving to 80: 96.6%

CURVE CHARACTERISTICS:
• Type: Type II (Diagonal)
• Compression: Moderate
• Rectangularization Index: 0.85

The survival curve follows Gompertz law after age 30.
Data sourced from 183,254 death certificates.


Instruction: Show survival curve for Japan male in 2018

Response:
SURVIVAL CURVE ANALYSIS

Population: Japan Male
Reference Year: 2018
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         82.0
    1          99,997           16         0.00016         74.9
    5          99,981           28         0.00028         78.6
   10          99,953           80         0.00080         66.6
   20          99,873          136         0.00136         60.0
   30          99,737          250         0.00251         46.5
   40          99,487          488         0.00491         40.4
   50          98,999          543         0.00548         26.5
   60          98,456          984         0.00999         15.6
   70          97,472        1,378         0.01414         12.4
   80          96,094        1,777         0.01849          0.0
   90          94,317        2,706         0.02869          2.5
  100          91,611        3,472         0.03790          4.5
  110          88,139       88,139         1.00000          2.3

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 80.6 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.5%
• Probability of Surviving to 80: 96.1%

CURVE CHARACTERISTICS:
• Type: Type I (Rectangular)
• Compression: High
• Rectangularization Index: 0.86

The survival curve follows Gompertz law after age 30.
Data sourced from 365,334 death certificates.

Human: Show survival curve for Japan male in 2018

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Japan Male
Reference Year: 2018
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            3         0.00003         82.0
    1          99,997           16         0.00016         74.9
    5          99,981           28         0.00028         78.6
   10          99,953           80         0.00080         66.6
   20          99,873          136         0.00136         60.0
   30          99,737          250         0.00251         46.5
   40          99,487          488         0.00491         40.4
   50          98,999          543         0.00548         26.5
   60          98,456          984         0.00999         15.6
   70          97,472        1,378         0.01414         12.4
   80          96,094        1,777         0.01849          0.0
   90          94,317        2,706         0.02869          2.5
  100          91,611        3,472         0.03790          4.5
  110          88,139       88,139         1.00000          2.3

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 80.6 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.5%
• Probability of Surviving to 80: 96.1%

CURVE CHARACTERISTICS:
• Type: Type I (Rectangular)
• Compression: High
• Rectangularization Index: 0.86

The survival curve follows Gompertz law after age 30.
Data sourced from 365,334 death certificates.


Instruction: Compare suburban vs other area mortality rates in UK

Response:
GEOGRAPHIC MORTALITY ANALYSIS

Country: UK
Focus: Suburban Areas

MORTALITY RATES (per 100,000):
• Urban: 837.6
• Rural: 966.7
• Suburban: 808.5

Rural areas show 15.4% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.

Human: Compare suburban vs other area mortality rates in UK

Actuarial AI: GEOGRAPHIC MORTALITY ANALYSIS

Country: UK
Focus: Suburban Areas

MORTALITY RATES (per 100,000):
• Urban: 837.6
• Rural: 966.7
• Suburban: 808.5

Rural areas show 15.4% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.


Instruction: Calculate Term life insurance premium for 46 year old female, $100,000 coverage, 15 year term, Standard rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $100,000
• Term Length: 15 years
• Issue Age: 46
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_46): 0.002022
• Underwriting Multiplier: 1.0x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 96% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $121.33
• Expense Charge: $30.33
• Reserve Accumulation: $40.44
• Profit Margin: $10.11
• Gross Annual Premium: $202.21

PAYMENT OPTIONS:
• Annual: $202.21
• Semi-Annual: $105.15 (x2 = $210.30/year)
• Quarterly: $53.59 (x4 = $214.34/year)
• Monthly: $18.20 (x12 = $218.39/year)

RESERVE CALCULATIONS:
• Net Level Premium: $151.66
• First Year Reserve: $40.44
• Terminal Reserve (Year 15): $41981.32

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

Internal Rate of Return: 10.8%
Profit Margin: 11.1%
Lapse Assumption: 7.2% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Term life insurance premium for 46 year old female, $100,000 coverage, 15 year term, Standard rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Term Life Insurance
• Face Amount: $100,000
• Term Length: 15 years
• Issue Age: 46
• Sex: Female
• Underwriting Class: Standard

PREMIUM COMPUTATION:
• Base Mortality Rate (q_46): 0.002022
• Underwriting Multiplier: 1.0x
• Product Load Factor: 1.0x
• Expense Loading: 15% of gross premium
• Commission Load: 96% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $121.33
• Expense Charge: $30.33
• Reserve Accumulation: $40.44
• Profit Margin: $10.11
• Gross Annual Premium: $202.21

PAYMENT OPTIONS:
• Annual: $202.21
• Semi-Annual: $105.15 (x2 = $210.30/year)
• Quarterly: $53.59 (x4 = $214.34/year)
• Monthly: $18.20 (x12 = $218.39/year)

RESERVE CALCULATIONS:
• Net Level Premium: $151.66
• First Year Reserve: $40.44
• Terminal Reserve (Year 15): $41981.32

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

Internal Rate of Return: 10.8%
Profit Margin: 11.1%
Lapse Assumption: 7.2% annual

Illustration assumes guaranteed rates. Actual results may vary.


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

Response:
LIFE INSURANCE PREMIUM CALCULATION

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

PREMIUM COMPUTATION:
• Base Mortality Rate (q_24): 0.001314
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 99% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $2207.56
• Expense Charge: $551.89
• Reserve Accumulation: $735.85
• Profit Margin: $183.96
• Gross Annual Premium: $3679.27

PAYMENT OPTIONS:
• Annual: $3679.27
• Semi-Annual: $1913.22 (x2 = $3826.44/year)
• Quarterly: $975.01 (x4 = $3900.03/year)
• Monthly: $331.13 (x12 = $3973.61/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2759.45
• First Year Reserve: $735.85
• Terminal Reserve (Year 41): $434300.38

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

Internal Rate of Return: 8.4%
Profit Margin: 11.1%
Lapse Assumption: 6.9% annual

Illustration assumes guaranteed rates. Actual results may vary.

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

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

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

PREMIUM COMPUTATION:
• Base Mortality Rate (q_24): 0.001314
• Underwriting Multiplier: 1.0x
• Product Load Factor: 2.8x
• Expense Loading: 15% of gross premium
• Commission Load: 99% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $2207.56
• Expense Charge: $551.89
• Reserve Accumulation: $735.85
• Profit Margin: $183.96
• Gross Annual Premium: $3679.27

PAYMENT OPTIONS:
• Annual: $3679.27
• Semi-Annual: $1913.22 (x2 = $3826.44/year)
• Quarterly: $975.01 (x4 = $3900.03/year)
• Monthly: $331.13 (x12 = $3973.61/year)

RESERVE CALCULATIONS:
• Net Level Premium: $2759.45
• First Year Reserve: $735.85
• Terminal Reserve (Year 41): $434300.38

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

Internal Rate of Return: 8.4%
Profit Margin: 11.1%
Lapse Assumption: 6.9% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: Calculate Whole Life life insurance premium for 26 year old female, $500,000 coverage, Standard Plus rating

Response:
LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $500,000
• Duration: Lifetime Coverage
• Issue Age: 26
• Sex: Female
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_26): 0.000934
• Underwriting Multiplier: 0.9x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 93% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $981.09
• Expense Charge: $245.27
• Reserve Accumulation: $327.03
• Profit Margin: $81.76
• Gross Annual Premium: $1635.15

PAYMENT OPTIONS:
• Annual: $1635.15
• Semi-Annual: $850.28 (x2 = $1700.56/year)
• Quarterly: $433.32 (x4 = $1733.26/year)
• Monthly: $147.16 (x12 = $1765.97/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1226.36
• First Year Reserve: $327.03
• Terminal Reserve (Year 39): $218758.13

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

Internal Rate of Return: 9.9%
Profit Margin: 14.7%
Lapse Assumption: 6.6% annual

Illustration assumes guaranteed rates. Actual results may vary.

Human: Calculate Whole Life life insurance premium for 26 year old female, $500,000 coverage, Standard Plus rating

Actuarial AI: LIFE INSURANCE PREMIUM CALCULATION

Policy Details:
• Product Type: Whole Life Life Insurance
• Face Amount: $500,000
• Duration: Lifetime Coverage
• Issue Age: 26
• Sex: Female
• Underwriting Class: Standard Plus

PREMIUM COMPUTATION:
• Base Mortality Rate (q_26): 0.000934
• Underwriting Multiplier: 0.9x
• Product Load Factor: 3.5x
• Expense Loading: 15% of gross premium
• Commission Load: 93% first year, 5% renewal

ANNUAL PREMIUM BREAKDOWN:
• Mortality Cost: $981.09
• Expense Charge: $245.27
• Reserve Accumulation: $327.03
• Profit Margin: $81.76
• Gross Annual Premium: $1635.15

PAYMENT OPTIONS:
• Annual: $1635.15
• Semi-Annual: $850.28 (x2 = $1700.56/year)
• Quarterly: $433.32 (x4 = $1733.26/year)
• Monthly: $147.16 (x12 = $1765.97/year)

RESERVE CALCULATIONS:
• Net Level Premium: $1226.36
• First Year Reserve: $327.03
• Terminal Reserve (Year 39): $218758.13

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

Internal Rate of Return: 9.9%
Profit Margin: 14.7%
Lapse Assumption: 6.6% annual

Illustration assumes guaranteed rates. Actual results may vary.


Instruction: What is the probability of death within 5 years for someone age 87?

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 87 years
• Assessment Period: 5 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_87): 0.003002 (0.3002%)
• 5-Year Death Probability (₍5₎q_87): 0.014922 (1.492%)
• Survival Probability (₍5₎p_87): 0.985078 (98.508%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_87): 0.003007
• Hazard Rate (h_87): 0.003007
• Cumulative Hazard (H_87): 0.015035
• Median Future Lifetime: 230.5 years

RISK CLASSIFICATION:
• Mortality Ratio: 3.0x standard
• Risk Category: Standard Plus
• Insurability: Standard or better
• Recommended Premium Loading: 200%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.012684
• Upper Bound: 0.017161

Analysis based on 176,903 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: What is the probability of death within 5 years for someone age 87?

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 87 years
• Assessment Period: 5 years
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: None reported

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_87): 0.003002 (0.3002%)
• 5-Year Death Probability (₍5₎q_87): 0.014922 (1.492%)
• Survival Probability (₍5₎p_87): 0.985078 (98.508%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_87): 0.003007
• Hazard Rate (h_87): 0.003007
• Cumulative Hazard (H_87): 0.015035
• Median Future Lifetime: 230.5 years

RISK CLASSIFICATION:
• Mortality Ratio: 3.0x standard
• Risk Category: Standard Plus
• Insurability: Standard or better
• Recommended Premium Loading: 200%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.012684
• Upper Bound: 0.017161

Analysis based on 176,903 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Calculate policy reserve for 67 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: 57
• Current Age: 67
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1324.08
• Present Value Future Benefits (PVFB): $51551.50
• Present Value Future Premiums (PVFP): $34044.19

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $13939.75
• Per $1,000 Face: $139.40

PROSPECTIVE METHOD:
• A₁_67:10⌉ = 0.2313
• ä_67:10⌉ = 8.0212
• ₁₀V = 100,000 × A₁ - P × ä = $13939.75

RETROSPECTIVE METHOD:
• Accumulated Premiums: $11569.32
• Accumulated Cost of Insurance: $4935.00
• Interest Earned: $1116.66
• ₁₀V = $13939.75

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $13242.76
• Tax Reserve: $12824.57
• GAAP Reserve: $14636.74

Human: Calculate policy reserve for 67 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: 57
• Current Age: 67
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1324.08
• Present Value Future Benefits (PVFB): $51551.50
• Present Value Future Premiums (PVFP): $34044.19

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $13939.75
• Per $1,000 Face: $139.40

PROSPECTIVE METHOD:
• A₁_67:10⌉ = 0.2313
• ä_67:10⌉ = 8.0212
• ₁₀V = 100,000 × A₁ - P × ä = $13939.75

RETROSPECTIVE METHOD:
• Accumulated Premiums: $11569.32
• Accumulated Cost of Insurance: $4935.00
• Interest Earned: $1116.66
• ₁₀V = $13939.75

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $13242.76
• Tax Reserve: $12824.57
• GAAP Reserve: $14636.74


Instruction: Show survival curve for Brazil female in 2016

Response:
SURVIVAL CURVE ANALYSIS

Population: Brazil Female
Reference Year: 2016
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         79.2
    1          99,998           10         0.00010         77.3
    5          99,988           25         0.00025         71.2
   10          99,963           51         0.00051         71.4
   20          99,912           97         0.00097         55.3
   30          99,815          177         0.00177         46.0
   40          99,638          291         0.00292         42.4
   50          99,347          389         0.00392         34.8
   60          98,958          792         0.00800         21.0
   70          98,166          836         0.00852         13.0
   80          97,330        1,281         0.01316          0.0
   90          96,049        2,203         0.02294          4.0
  100          93,846        3,292         0.03508          2.5
  110          90,554       90,554         1.00000          2.0

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 82.5 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 99.0%
• Probability of Surviving to 80: 97.3%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 158,271 death certificates.

Human: Show survival curve for Brazil female in 2016

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Brazil Female
Reference Year: 2016
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         79.2
    1          99,998           10         0.00010         77.3
    5          99,988           25         0.00025         71.2
   10          99,963           51         0.00051         71.4
   20          99,912           97         0.00097         55.3
   30          99,815          177         0.00177         46.0
   40          99,638          291         0.00292         42.4
   50          99,347          389         0.00392         34.8
   60          98,958          792         0.00800         21.0
   70          98,166          836         0.00852         13.0
   80          97,330        1,281         0.01316          0.0
   90          96,049        2,203         0.02294          4.0
  100          93,846        3,292         0.03508          2.5
  110          90,554       90,554         1.00000          2.0

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 82.5 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 99.0%
• Probability of Surviving to 80: 97.3%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 158,271 death certificates.


Instruction: Compare life expectancy between China, Canada, South Korea and Japan

Response:
INTERNATIONAL MORTALITY COMPARISON

Metric: Life Expectancy
Countries: China, Canada, South Korea, Japan
Reference Year: 2020

COMPARATIVE STATISTICS:
• China: 74.4 years
• Canada: 80.0 years
• South Korea: 76.1 years
• Japan: 77.1 years

RANKINGS:
1. Canada: 80.0
2. Japan: 77.1
3. South Korea: 76.1
4. China: 74.4

STATISTICAL ANALYSIS:
• Range: 5.6
• Mean: 76.9
• Median: 76.6
• Standard Deviation: 2.0
• Coefficient of Variation: 2.6%

RELATIVE COMPARISONS:
• Best vs Worst: 0.93x difference
• Above Average: 2/4
• Global Ranking: China: #94, Canada: #79, South Korea: #109

CONTRIBUTING FACTORS:
• Healthcare System: 27% of variation
• Economic Development: 34% of variation
• Public Health Policy: 11% of variation
• Demographics: 12% of variation
• Environmental Factors: 6% of variation

Convergence/Divergence: Converging at 0.8% annually

Human: Compare life expectancy between China, Canada, South Korea and Japan

Actuarial AI: INTERNATIONAL MORTALITY COMPARISON

Metric: Life Expectancy
Countries: China, Canada, South Korea, Japan
Reference Year: 2020

COMPARATIVE STATISTICS:
• China: 74.4 years
• Canada: 80.0 years
• South Korea: 76.1 years
• Japan: 77.1 years

RANKINGS:
1. Canada: 80.0
2. Japan: 77.1
3. South Korea: 76.1
4. China: 74.4

STATISTICAL ANALYSIS:
• Range: 5.6
• Mean: 76.9
• Median: 76.6
• Standard Deviation: 2.0
• Coefficient of Variation: 2.6%

RELATIVE COMPARISONS:
• Best vs Worst: 0.93x difference
• Above Average: 2/4
• Global Ranking: China: #94, Canada: #79, South Korea: #109

CONTRIBUTING FACTORS:
• Healthcare System: 27% of variation
• Economic Development: 34% of variation
• Public Health Policy: 11% of variation
• Demographics: 12% of variation
• Environmental Factors: 6% of variation

Convergence/Divergence: Converging at 0.8% annually


Instruction: Calculate policy reserve for 39 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: 29
• Current Age: 39
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1098.69
• Present Value Future Benefits (PVFB): $51395.24
• Present Value Future Premiums (PVFP): $23997.39

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $10248.52
• Per $1,000 Face: $102.49

PROSPECTIVE METHOD:
• A₁_39:10⌉ = 0.2277
• ä_39:10⌉ = 8.6318
• ₁₀V = 100,000 × A₁ - P × ä = $10248.52

RETROSPECTIVE METHOD:
• Accumulated Premiums: $11003.15
• Accumulated Cost of Insurance: $5880.36
• Interest Earned: $1443.63
• ₁₀V = $10248.52

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $9736.10
• Tax Reserve: $9428.64
• GAAP Reserve: $10760.95

Human: Calculate policy reserve for 39 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: 29
• Current Age: 39
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1098.69
• Present Value Future Benefits (PVFB): $51395.24
• Present Value Future Premiums (PVFP): $23997.39

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $10248.52
• Per $1,000 Face: $102.49

PROSPECTIVE METHOD:
• A₁_39:10⌉ = 0.2277
• ä_39:10⌉ = 8.6318
• ₁₀V = 100,000 × A₁ - P × ä = $10248.52

RETROSPECTIVE METHOD:
• Accumulated Premiums: $11003.15
• Accumulated Cost of Insurance: $5880.36
• Interest Earned: $1443.63
• ₁₀V = $10248.52

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $9736.10
• Tax Reserve: $9428.64
• GAAP Reserve: $10760.95


Instruction: Summarize individual life mortality experience study results

Response:
MORTALITY EXPERIENCE STUDY

Study Type: Individual Life Insurance
Study Period: 2021-2023
Exposure: 764112 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 0.97
• Deaths Actual: 8,086
• Deaths Expected: 4,885

BY DURATION:
• Select Period (Years 1-5): 0.85
• Ultimate (Years 6+): 1.01

Statistical confidence: 95% CI [0.94, 1.17]

Human: Summarize individual life mortality experience study results

Actuarial AI: MORTALITY EXPERIENCE STUDY

Study Type: Individual Life Insurance
Study Period: 2021-2023
Exposure: 764112 life-years

ACTUAL vs EXPECTED:
• Overall A/E Ratio: 0.97
• Deaths Actual: 8,086
• Deaths Expected: 4,885

BY DURATION:
• Select Period (Years 1-5): 0.85
• Ultimate (Years 6+): 1.01

Statistical confidence: 95% CI [0.94, 1.17]


Instruction: Analyze mortality differences by education in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Education
Country: USA
Analysis Period: 2020

MORTALITY RATES BY EDUCATION (per 100,000):
• Less than High School: 714.1
• High School: 842.8
• Some College: 826.0
• Bachelor's: 643.1
• Graduate Degree: 368.5

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.92
• Rate Difference: 312.1 per 100,000
• Population Attributable Risk: 37.5%
• Gini Coefficient: 0.316

LIFE EXPECTANCY BY EDUCATION:
• Less than High School: 83.8 years
• High School: 80.2 years
• Some College: 71.3 years
• Bachelor's: 76.5 years
• Graduate Degree: 71.3 years

CONTRIBUTING FACTORS:
• Healthcare Access: 32% of disparity
• Socioeconomic Status: 29% of disparity
• Environmental Factors: 16% of disparity
• Behavioral Factors: 22% of disparity
• Biological Factors: 13% of disparity

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

Social determinants explain 64% of observed mortality differences.

Human: Analyze mortality differences by education in the USA

Actuarial AI: DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Education
Country: USA
Analysis Period: 2020

MORTALITY RATES BY EDUCATION (per 100,000):
• Less than High School: 714.1
• High School: 842.8
• Some College: 826.0
• Bachelor's: 643.1
• Graduate Degree: 368.5

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 2.92
• Rate Difference: 312.1 per 100,000
• Population Attributable Risk: 37.5%
• Gini Coefficient: 0.316

LIFE EXPECTANCY BY EDUCATION:
• Less than High School: 83.8 years
• High School: 80.2 years
• Some College: 71.3 years
• Bachelor's: 76.5 years
• Graduate Degree: 71.3 years

CONTRIBUTING FACTORS:
• Healthcare Access: 32% of disparity
• Socioeconomic Status: 29% of disparity
• Environmental Factors: 16% of disparity
• Behavioral Factors: 22% of disparity
• Biological Factors: 13% of disparity

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

Social determinants explain 64% of observed mortality differences.


Instruction: Calculate policy reserve for 48 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: 38
• Current Age: 48
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $700.11
• Present Value Future Benefits (PVFB): $47706.05
• Present Value Future Premiums (PVFP): $32547.82

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $34497.32
• Per $1,000 Face: $344.97

PROSPECTIVE METHOD:
• A₁_48:10⌉ = 0.1545
• ä_48:10⌉ = 9.3215
• ₁₀V = 100,000 × A₁ - P × ä = $34497.32

RETROSPECTIVE METHOD:
• Accumulated Premiums: $11093.92
• Accumulated Cost of Insurance: $5474.82
• Interest Earned: $1002.80
• ₁₀V = $34497.32

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $32772.45
• Tax Reserve: $31737.53
• GAAP Reserve: $36222.19

Human: Calculate policy reserve for 48 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: 38
• Current Age: 48
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $700.11
• Present Value Future Benefits (PVFB): $47706.05
• Present Value Future Premiums (PVFP): $32547.82

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $34497.32
• Per $1,000 Face: $344.97

PROSPECTIVE METHOD:
• A₁_48:10⌉ = 0.1545
• ä_48:10⌉ = 9.3215
• ₁₀V = 100,000 × A₁ - P × ä = $34497.32

RETROSPECTIVE METHOD:
• Accumulated Premiums: $11093.92
• Accumulated Cost of Insurance: $5474.82
• Interest Earned: $1002.80
• ₁₀V = $34497.32

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $32772.45
• Tax Reserve: $31737.53
• GAAP Reserve: $36222.19


Instruction: Mortality risk assessment for 38 year old over next 1 years

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 38 years
• Assessment Period: 1 year
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: hypertension, obesity, cancer history

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_38): 0.004544 (0.4544%)
• 1-Year Death Probability (₍1₎q_38): 0.004544 (0.454%)
• Survival Probability (₍1₎p_38): 0.995456 (99.546%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_38): 0.004554
• Hazard Rate (h_38): 0.004554
• Cumulative Hazard (H_38): 0.004554
• Median Future Lifetime: 152.2 years

RISK CLASSIFICATION:
• Mortality Ratio: 4.5x standard
• Risk Category: Standard
• Insurability: Substandard with exclusions
• Recommended Premium Loading: 354%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.003862
• Upper Bound: 0.005225

Analysis based on 111,046 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Mortality risk assessment for 38 year old over next 1 years

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 38 years
• Assessment Period: 1 year
• Smoking Status: Smoker (2.5x mortality multiplier)
• Health Conditions: hypertension, obesity, cancer history

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_38): 0.004544 (0.4544%)
• 1-Year Death Probability (₍1₎q_38): 0.004544 (0.454%)
• Survival Probability (₍1₎p_38): 0.995456 (99.546%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_38): 0.004554
• Hazard Rate (h_38): 0.004554
• Cumulative Hazard (H_38): 0.004554
• Median Future Lifetime: 152.2 years

RISK CLASSIFICATION:
• Mortality Ratio: 4.5x standard
• Risk Category: Standard
• Insurability: Substandard with exclusions
• Recommended Premium Loading: 354%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.003862
• Upper Bound: 0.005225

Analysis based on 111,046 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Calculate the present value of a life annuity for a 58 year old at 4.8% interest

Response:
LIFE ANNUITY VALUATION

Parameters:
• Age (x): 58
• Interest Rate (i): 4.85%
• Discount Factor (v): 0.953769
• Mortality Table: 2017 CSO

ANNUITY VALUES:
• Whole Life Annuity-Due (ä_58): 17.1186
• Whole Life Annuity-Immediate (a_58): 16.1186
• Temporary Annuity-Due (ä_58:20⌉): 15.1528
• Deferred Annuity (₁₀|ä_58): 9.4721

COMMUTATION FUNCTIONS:
• D_58 = v^58 × l_58: 2139.47
• N_58 = Σ D_k (k≥58): 28832.28
• S_58 = Σ N_k (k≥58): 272325.22

CALCULATION:
ä_58 = N_58 / D_58 = 17.1186

MONTHLY CONVERSION:
• Annual Annuity: $10000.00
• Monthly Payment: $837.17
• Conversion Factor (12): 11.733

Present Value of $1,000/month for life: $16738242.53

Human: Calculate the present value of a life annuity for a 58 year old at 4.8% interest

Actuarial AI: LIFE ANNUITY VALUATION

Parameters:
• Age (x): 58
• Interest Rate (i): 4.85%
• Discount Factor (v): 0.953769
• Mortality Table: 2017 CSO

ANNUITY VALUES:
• Whole Life Annuity-Due (ä_58): 17.1186
• Whole Life Annuity-Immediate (a_58): 16.1186
• Temporary Annuity-Due (ä_58:20⌉): 15.1528
• Deferred Annuity (₁₀|ä_58): 9.4721

COMMUTATION FUNCTIONS:
• D_58 = v^58 × l_58: 2139.47
• N_58 = Σ D_k (k≥58): 28832.28
• S_58 = Σ N_k (k≥58): 272325.22

CALCULATION:
ä_58 = N_58 / D_58 = 17.1186

MONTHLY CONVERSION:
• Annual Annuity: $10000.00
• Monthly Payment: $837.17
• Conversion Factor (12): 11.733

Present Value of $1,000/month for life: $16738242.53


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

Response:
OCCUPATIONAL MORTALITY ANALYSIS

Industry: Manufacturing
Fatal Injury Rate: 42.3 per 100,000 full-time workers
Annual Deaths: 1,882

LEADING CAUSES:
• Falls: 21%
• Struck by object: 23%
• Electrocution: 6%
• Caught-in/between: 20%

Workers' compensation death benefit: $396,029

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

Actuarial AI: OCCUPATIONAL MORTALITY ANALYSIS

Industry: Manufacturing
Fatal Injury Rate: 42.3 per 100,000 full-time workers
Annual Deaths: 1,882

LEADING CAUSES:
• Falls: 21%
• Struck by object: 23%
• Electrocution: 6%
• Caught-in/between: 20%

Workers' compensation death benefit: $396,029


Instruction: What is the mortality rate for Alzheimer's in Australia for Under 25 in 2019?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Alzheimer's
Location: Australia
Year: 2019
Age Group: Under 25

MORTALITY STATISTICS:
• Crude Death Rate: 22.5 per 100,000 population
• Age-Adjusted Rate: 19.6 per 100,000
• Total Deaths: 753,377
• Percentage of All Deaths: 9.0%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 27.0 per 100,000
• Female Death Rate: 19.1 per 100,000
• Sex Ratio (M:F): 1.41:1

TREND ANALYSIS:
• 5-Year Change: +11.0%
• 10-Year Change: +23.0%
• Annual Percentage Change: +0.8%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #15
• Years of Potential Life Lost (YPLL): 21168827
• Economic Burden: $30.4 billion annually
• Preventable Deaths: 53%

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

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

Human: What is the mortality rate for Alzheimer's in Australia for Under 25 in 2019?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Alzheimer's
Location: Australia
Year: 2019
Age Group: Under 25

MORTALITY STATISTICS:
• Crude Death Rate: 22.5 per 100,000 population
• Age-Adjusted Rate: 19.6 per 100,000
• Total Deaths: 753,377
• Percentage of All Deaths: 9.0%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 27.0 per 100,000
• Female Death Rate: 19.1 per 100,000
• Sex Ratio (M:F): 1.41:1

TREND ANALYSIS:
• 5-Year Change: +11.0%
• 10-Year Change: +23.0%
• Annual Percentage Change: +0.8%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #15
• Years of Potential Life Lost (YPLL): 21168827
• Economic Burden: $30.4 billion annually
• Preventable Deaths: 53%

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

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


Instruction: Analyze mortality differences by occupation in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Occupation
Country: USA
Analysis Period: 2021

MORTALITY RATES BY OCCUPATION (per 100,000):
• Healthcare: 579.9
• Construction: 558.9
• Office: 1125.7
• Transportation: 915.6
• Service: 915.6

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.96
• Rate Difference: 654.0 per 100,000
• Population Attributable Risk: 13.9%
• Gini Coefficient: 0.153

LIFE EXPECTANCY BY OCCUPATION:
• Healthcare: 76.3 years
• Construction: 72.6 years
• Office: 79.3 years
• Transportation: 83.2 years
• Service: 75.6 years

CONTRIBUTING FACTORS:
• Healthcare Access: 24% of disparity
• Socioeconomic Status: 29% of disparity
• Environmental Factors: 13% of disparity
• Behavioral Factors: 10% of disparity
• Biological Factors: 10% of disparity

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

Social determinants explain 62% of observed mortality differences.

Human: Analyze mortality differences by occupation in the USA

Actuarial AI: DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Occupation
Country: USA
Analysis Period: 2021

MORTALITY RATES BY OCCUPATION (per 100,000):
• Healthcare: 579.9
• Construction: 558.9
• Office: 1125.7
• Transportation: 915.6
• Service: 915.6

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.96
• Rate Difference: 654.0 per 100,000
• Population Attributable Risk: 13.9%
• Gini Coefficient: 0.153

LIFE EXPECTANCY BY OCCUPATION:
• Healthcare: 76.3 years
• Construction: 72.6 years
• Office: 79.3 years
• Transportation: 83.2 years
• Service: 75.6 years

CONTRIBUTING FACTORS:
• Healthcare Access: 24% of disparity
• Socioeconomic Status: 29% of disparity
• Environmental Factors: 13% of disparity
• Behavioral Factors: 10% of disparity
• Biological Factors: 10% of disparity

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

Social determinants explain 62% of observed mortality differences.


Instruction: Show survival curve for Germany female in 2023

Response:
SURVIVAL CURVE ANALYSIS

Population: Germany Female
Reference Year: 2023
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         78.6
    1          99,998           10         0.00010         78.2
    5          99,988           21         0.00021         74.7
   10          99,967           63         0.00063         67.7
   20          99,904           93         0.00093         59.6
   30          99,811          161         0.00161         49.6
   40          99,650          312         0.00313         39.9
   50          99,338          444         0.00447         27.1
   60          98,894          655         0.00662         16.4
   70          98,239          813         0.00828          5.1
   80          97,426        1,282         0.01316          0.0
   90          96,144        1,967         0.02046          1.3
  100          94,177        3,035         0.03223          1.1
  110          91,142       91,142         1.00000          2.4

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 83.7 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.4%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 377,161 death certificates.

Human: Show survival curve for Germany female in 2023

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Germany Female
Reference Year: 2023
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         78.6
    1          99,998           10         0.00010         78.2
    5          99,988           21         0.00021         74.7
   10          99,967           63         0.00063         67.7
   20          99,904           93         0.00093         59.6
   30          99,811          161         0.00161         49.6
   40          99,650          312         0.00313         39.9
   50          99,338          444         0.00447         27.1
   60          98,894          655         0.00662         16.4
   70          98,239          813         0.00828          5.1
   80          97,426        1,282         0.01316          0.0
   90          96,144        1,967         0.02046          1.3
  100          94,177        3,035         0.03223          1.1
  110          91,142       91,142         1.00000          2.4

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 83.7 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.9%
• Probability of Surviving to 80: 97.4%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 377,161 death certificates.


Instruction: Show survival curve for Canada female in 2020

Response:
SURVIVAL CURVE ANALYSIS

Population: Canada Female
Reference Year: 2020
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         75.1
    1          99,998            9         0.00009         84.0
    5          99,989           22         0.00022         70.5
   10          99,967           59         0.00059         70.1
   20          99,908          107         0.00107         59.9
   30          99,801          199         0.00199         48.2
   40          99,602          355         0.00356         39.0
   50          99,247          484         0.00488         33.7
   60          98,763          767         0.00777         22.0
   70          97,996        1,145         0.01168          7.9
   80          96,851        1,587         0.01639          0.0
   90          95,264        2,139         0.02245          1.9
  100          93,125        2,655         0.02851          1.1
  110          90,470       90,470         1.00000          2.8

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 78.5 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.8%
• Probability of Surviving to 80: 96.9%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 369,942 death certificates.

Human: Show survival curve for Canada female in 2020

Actuarial AI: SURVIVAL CURVE ANALYSIS

Population: Canada Female
Reference Year: 2020
Initial Cohort: 100,000 births

SURVIVAL TABLE (l_x per 100,000):
  Age  Survivors (lx)  Deaths (dx) Prob Death (qx) Life Exp (ex)
============================================================
    0         100,000            2         0.00002         75.1
    1          99,998            9         0.00009         84.0
    5          99,989           22         0.00022         70.5
   10          99,967           59         0.00059         70.1
   20          99,908          107         0.00107         59.9
   30          99,801          199         0.00199         48.2
   40          99,602          355         0.00356         39.0
   50          99,247          484         0.00488         33.7
   60          98,763          767         0.00777         22.0
   70          97,996        1,145         0.01168          7.9
   80          96,851        1,587         0.01639          0.0
   90          95,264        2,139         0.02245          1.9
  100          93,125        2,655         0.02851          1.1
  110          90,470       90,470         1.00000          2.8

SURVIVAL METRICS:
• Median Survival Age: 110 years
• Life Expectancy at Birth: 78.5 years
• Infant Mortality Rate: 0.0 per 1,000
• Probability of Surviving to 65: 98.8%
• Probability of Surviving to 80: 96.9%

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

The survival curve follows Gompertz law after age 30.
Data sourced from 369,942 death certificates.


Instruction: Analyze mortality trends in Germany from 2010-2021

Response:
MORTALITY TREND ANALYSIS

Country: Germany
Analysis Period: 2010-2021

OVERALL TRENDS:
• Average Annual Change: +1.8%
• Total Change: +20.2%
• Trend Direction: Worsening
• Statistical Significance: p < 0.001

Life expectancy increased by 1.1 years.
Age-standardized death rate changed by +158 per 100,000.

KEY DRIVERS:
• Medical advances: 23% of improvement
• Public health measures: 28%
• Lifestyle changes: +20%
• Environmental factors: -14%

Human: Analyze mortality trends in Germany from 2010-2021

Actuarial AI: MORTALITY TREND ANALYSIS

Country: Germany
Analysis Period: 2010-2021

OVERALL TRENDS:
• Average Annual Change: +1.8%
• Total Change: +20.2%
• Trend Direction: Worsening
• Statistical Significance: p < 0.001

Life expectancy increased by 1.1 years.
Age-standardized death rate changed by +158 per 100,000.

KEY DRIVERS:
• Medical advances: 23% of improvement
• Public health measures: 28%
• Lifestyle changes: +20%
• Environmental factors: -14%


Instruction: Project mortality rates for Japan in 2030

Response:
MORTALITY PROJECTION

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

PROJECTED METRICS:
• Crude Death Rate: 814.9 per 100,000
• Life Expectancy: 87.7 years
• Annual Improvement: 0.93%

CONFIDENCE INTERVALS (95%):
• Lower: 692.7
• Upper: 937.2

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

Human: Project mortality rates for Japan in 2030

Actuarial AI: MORTALITY PROJECTION

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

PROJECTED METRICS:
• Crude Death Rate: 814.9 per 100,000
• Life Expectancy: 87.7 years
• Annual Improvement: 0.93%

CONFIDENCE INTERVALS (95%):
• Lower: 692.7
• Upper: 937.2

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


Instruction: Analyze mortality differences by race in the USA

Response:
DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Race
Country: USA
Analysis Period: 2019

MORTALITY RATES BY RACE (per 100,000):
• White: 406.2
• Black: 1112.1
• Asian: 905.6
• Hispanic: 655.2
• Native American: 1092.0

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.74
• Rate Difference: 543.0 per 100,000
• Population Attributable Risk: 31.3%
• Gini Coefficient: 0.153

LIFE EXPECTANCY BY RACE:
• White: 80.4 years
• Black: 83.4 years
• Asian: 75.6 years
• Hispanic: 81.6 years
• Native American: 70.0 years

CONTRIBUTING FACTORS:
• Healthcare Access: 37% of disparity
• Socioeconomic Status: 34% of disparity
• Environmental Factors: 19% of disparity
• Behavioral Factors: 19% of disparity
• Biological Factors: 8% of disparity

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

Social determinants explain 69% of observed mortality differences.

Human: Analyze mortality differences by race in the USA

Actuarial AI: DEMOGRAPHIC MORTALITY ANALYSIS

Demographic Variable: Race
Country: USA
Analysis Period: 2019

MORTALITY RATES BY RACE (per 100,000):
• White: 406.2
• Black: 1112.1
• Asian: 905.6
• Hispanic: 655.2
• Native American: 1092.0

DISPARITY METRICS:
• Rate Ratio (Highest/Lowest): 1.74
• Rate Difference: 543.0 per 100,000
• Population Attributable Risk: 31.3%
• Gini Coefficient: 0.153

LIFE EXPECTANCY BY RACE:
• White: 80.4 years
• Black: 83.4 years
• Asian: 75.6 years
• Hispanic: 81.6 years
• Native American: 70.0 years

CONTRIBUTING FACTORS:
• Healthcare Access: 37% of disparity
• Socioeconomic Status: 34% of disparity
• Environmental Factors: 19% of disparity
• Behavioral Factors: 19% of disparity
• Biological Factors: 8% of disparity

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

Social determinants explain 69% of observed mortality differences.


Instruction: What is the mortality rate for Diabetes in Canada for 45-64 in 2019?

Response:
CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Diabetes
Location: Canada
Year: 2019
Age Group: 45-64

MORTALITY STATISTICS:
• Crude Death Rate: 27.7 per 100,000 population
• Age-Adjusted Rate: 24.5 per 100,000
• Total Deaths: 592,675
• Percentage of All Deaths: 24.1%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 33.2 per 100,000
• Female Death Rate: 23.5 per 100,000
• Sex Ratio (M:F): 1.29:1

TREND ANALYSIS:
• 5-Year Change: -13.3%
• 10-Year Change: +17.1%
• Annual Percentage Change: +2.3%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #8
• Years of Potential Life Lost (YPLL): 9412065
• Economic Burden: $67.7 billion annually
• Preventable Deaths: 50%

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

International Classification of Diseases (ICD-10): E10-E14
Data Quality: Partial (89% coverage)

Human: What is the mortality rate for Diabetes in Canada for 45-64 in 2019?

Actuarial AI: CAUSE-SPECIFIC MORTALITY ANALYSIS

Cause of Death: Diabetes
Location: Canada
Year: 2019
Age Group: 45-64

MORTALITY STATISTICS:
• Crude Death Rate: 27.7 per 100,000 population
• Age-Adjusted Rate: 24.5 per 100,000
• Total Deaths: 592,675
• Percentage of All Deaths: 24.1%

DEMOGRAPHIC BREAKDOWN:
• Male Death Rate: 33.2 per 100,000
• Female Death Rate: 23.5 per 100,000
• Sex Ratio (M:F): 1.29:1

TREND ANALYSIS:
• 5-Year Change: -13.3%
• 10-Year Change: +17.1%
• Annual Percentage Change: +2.3%
• Trend: Increasing

COMPARATIVE METRICS:
• Rank Among Leading Causes: #8
• Years of Potential Life Lost (YPLL): 9412065
• Economic Burden: $67.7 billion annually
• Preventable Deaths: 50%

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

International Classification of Diseases (ICD-10): E10-E14
Data Quality: Partial (89% coverage)


Instruction: Analyze mortality trends in USA from 2005-2024

Response:
MORTALITY TREND ANALYSIS

Country: USA
Analysis Period: 2005-2024

OVERALL TRENDS:
• Average Annual Change: +0.5%
• Total Change: -6.8%
• Trend Direction: Worsening
• Statistical Significance: p < 0.001

Life expectancy increased by 2.2 years.
Age-standardized death rate changed by +186 per 100,000.

KEY DRIVERS:
• Medical advances: 27% of improvement
• Public health measures: 23%
• Lifestyle changes: +21%
• Environmental factors: +8%

Human: Analyze mortality trends in USA from 2005-2024

Actuarial AI: MORTALITY TREND ANALYSIS

Country: USA
Analysis Period: 2005-2024

OVERALL TRENDS:
• Average Annual Change: +0.5%
• Total Change: -6.8%
• Trend Direction: Worsening
• Statistical Significance: p < 0.001

Life expectancy increased by 2.2 years.
Age-standardized death rate changed by +186 per 100,000.

KEY DRIVERS:
• Medical advances: 27% of improvement
• Public health measures: 23%
• Lifestyle changes: +21%
• Environmental factors: +8%


Instruction: Compare urban vs other area mortality rates in UK

Response:
GEOGRAPHIC MORTALITY ANALYSIS

Country: UK
Focus: Urban Areas

MORTALITY RATES (per 100,000):
• Urban: 801.4
• Rural: 978.1
• Suburban: 739.3

Rural areas show 22.0% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.

Human: Compare urban vs other area mortality rates in UK

Actuarial AI: GEOGRAPHIC MORTALITY ANALYSIS

Country: UK
Focus: Urban Areas

MORTALITY RATES (per 100,000):
• Urban: 801.4
• Rural: 978.1
• Suburban: 739.3

Rural areas show 22.0% higher mortality.
Primary factors: healthcare access, emergency response times, demographics.


Instruction: Perform mortality assumption review for life insurance portfolio

Response:
MORTALITY ASSUMPTION VALUATION

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

CURRENT ASSUMPTIONS:
• Base Table: Pub-2010
• Improvement Scale: MP-2019
• Experience Adjustment: 95%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 1.00
• Credibility Factor: 0.95
• Indicated Change: +6.5%

FINANCIAL IMPACT:
• Reserve Change: $2.8 million
• Funded Ratio Impact: +1.7%

Recommendation: Maintain current assumptions

Human: Perform mortality assumption review for life insurance portfolio

Actuarial AI: MORTALITY ASSUMPTION VALUATION

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

CURRENT ASSUMPTIONS:
• Base Table: Pub-2010
• Improvement Scale: MP-2019
• Experience Adjustment: 95%

EXPERIENCE ANALYSIS:
• Actual/Expected Ratio: 1.00
• Credibility Factor: 0.95
• Indicated Change: +6.5%

FINANCIAL IMPACT:
• Reserve Change: $2.8 million
• Funded Ratio Impact: +1.7%

Recommendation: Maintain current assumptions


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

Response:
OCCUPATIONAL MORTALITY ANALYSIS

Industry: Manufacturing
Fatal Injury Rate: 129.8 per 100,000 full-time workers
Annual Deaths: 10,898

LEADING CAUSES:
• Falls: 27%
• Struck by object: 26%
• Electrocution: 8%
• Caught-in/between: 11%

Workers' compensation death benefit: $410,536

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

Actuarial AI: OCCUPATIONAL MORTALITY ANALYSIS

Industry: Manufacturing
Fatal Injury Rate: 129.8 per 100,000 full-time workers
Annual Deaths: 10,898

LEADING CAUSES:
• Falls: 27%
• Struck by object: 26%
• Electrocution: 8%
• Caught-in/between: 11%

Workers' compensation death benefit: $410,536


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

Response:
EXCESS MORTALITY ANALYSIS

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

MORTALITY METRICS:
• Expected Deaths (Baseline): 46,304
• Observed Deaths: 64,916
• Excess Deaths: 18,612
• Excess Mortality Rate: 40.2%
• P-score: 40.2%
• Z-score: 5.24 (p < 0.001)

BASELINE CALCULATION:
• Method: Farrington surveillance
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.7% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: -2.1% (1,861 deaths)
• 45-64 years: 19.1% (4,653 deaths)
• 65-74 years: 12.4% (4,653 deaths)
• 75+ years: 33.4% (7,444 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 10,387 (76%)
• Indirect (probable): 4,905 (19%)
• Collateral (delayed care): 2,050 (13%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [15,820, 21,403]
• Probability of chance: < 0.001
• Power: 0.95

Years of Life Lost: 263408
Economic Impact: $3.5 billion
Quality-Adjusted Life Years Lost: 211213

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

Actuarial AI: EXCESS MORTALITY ANALYSIS

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

MORTALITY METRICS:
• Expected Deaths (Baseline): 46,304
• Observed Deaths: 64,916
• Excess Deaths: 18,612
• Excess Mortality Rate: 40.2%
• P-score: 40.2%
• Z-score: 5.24 (p < 0.001)

BASELINE CALCULATION:
• Method: Farrington surveillance
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.7% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: -2.1% (1,861 deaths)
• 45-64 years: 19.1% (4,653 deaths)
• 65-74 years: 12.4% (4,653 deaths)
• 75+ years: 33.4% (7,444 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 10,387 (76%)
• Indirect (probable): 4,905 (19%)
• Collateral (delayed care): 2,050 (13%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [15,820, 21,403]
• Probability of chance: < 0.001
• Power: 0.95

Years of Life Lost: 263408
Economic Impact: $3.5 billion
Quality-Adjusted Life Years Lost: 211213


Instruction: Calculate excess mortality during COVID-19 pandemic in USA for 2022

Response:
EXCESS MORTALITY ANALYSIS

Event: COVID-19 pandemic
Location: USA
Period: 2022

MORTALITY METRICS:
• Expected Deaths (Baseline): 46,652
• Observed Deaths: 54,096
• Excess Deaths: 7,444
• Excess Mortality Rate: 16.0%
• P-score: 16.0%
• Z-score: 4.44 (p < 0.001)

BASELINE CALCULATION:
• Method: Serfling regression
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.2% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 0.8% (744 deaths)
• 45-64 years: 11.5% (1,861 deaths)
• 65-74 years: 12.5% (1,861 deaths)
• 75+ years: 37.8% (2,977 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 5,395 (64%)
• Indirect (probable): 1,969 (22%)
• Collateral (delayed care): 1,001 (12%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [6,327, 8,560]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 78511
Economic Impact: $6.7 billion
Quality-Adjusted Life Years Lost: 88709

Human: Calculate excess mortality during COVID-19 pandemic in USA for 2022

Actuarial AI: EXCESS MORTALITY ANALYSIS

Event: COVID-19 pandemic
Location: USA
Period: 2022

MORTALITY METRICS:
• Expected Deaths (Baseline): 46,652
• Observed Deaths: 54,096
• Excess Deaths: 7,444
• Excess Mortality Rate: 16.0%
• P-score: 16.0%
• Z-score: 4.44 (p < 0.001)

BASELINE CALCULATION:
• Method: Serfling regression
• Reference Period: 2015-2019
• Seasonal Adjustment: Applied
• Trend Adjustment: 2.2% annual

AGE-SPECIFIC EXCESS:
• 0-44 years: 0.8% (744 deaths)
• 45-64 years: 11.5% (1,861 deaths)
• 65-74 years: 12.5% (1,861 deaths)
• 75+ years: 37.8% (2,977 deaths)

CAUSE ATTRIBUTION:
• Direct (confirmed): 5,395 (64%)
• Indirect (probable): 1,969 (22%)
• Collateral (delayed care): 1,001 (12%)

STATISTICAL SIGNIFICANCE:
• 95% CI: [6,327, 8,560]
• Probability of chance: < 0.001
• Power: 0.98

Years of Life Lost: 78511
Economic Impact: $6.7 billion
Quality-Adjusted Life Years Lost: 88709


Instruction: Mortality risk assessment for 55 year old over next 1 years

Response:
MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 55 years
• Assessment Period: 1 year
• Smoking Status: Non-smoker
• Health Conditions: cancer history

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_55): 0.000842 (0.0842%)
• 1-Year Death Probability (₍1₎q_55): 0.000842 (0.084%)
• Survival Probability (₍1₎p_55): 0.999158 (99.916%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_55): 0.000842
• Hazard Rate (h_55): 0.000842
• Cumulative Hazard (H_55): 0.000842
• Median Future Lifetime: 823.1 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.8x standard
• Risk Category: Preferred Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.000715
• Upper Bound: 0.000968

Analysis based on 167,658 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.

Human: Mortality risk assessment for 55 year old over next 1 years

Actuarial AI: MORTALITY RISK ASSESSMENT

Subject Profile:
• Age: 55 years
• Assessment Period: 1 year
• Smoking Status: Non-smoker
• Health Conditions: cancer history

DEATH PROBABILITY CALCULATIONS:
• Annual Death Probability (q_55): 0.000842 (0.0842%)
• 1-Year Death Probability (₍1₎q_55): 0.000842 (0.084%)
• Survival Probability (₍1₎p_55): 0.999158 (99.916%)

DETAILED MORTALITY METRICS:
• Force of Mortality (μ_55): 0.000842
• Hazard Rate (h_55): 0.000842
• Cumulative Hazard (H_55): 0.000842
• Median Future Lifetime: 823.1 years

RISK CLASSIFICATION:
• Mortality Ratio: 0.8x standard
• Risk Category: Preferred Plus
• Insurability: Standard with loading
• Recommended Premium Loading: 0%

CONFIDENCE INTERVALS (95%):
• Lower Bound: 0.000715
• Upper Bound: 0.000968

Analysis based on 167,658 similar profiles.
Mortality follows Gompertz-Makeham law with parameters estimated via MLE.


Instruction: Calculate policy reserve for 32 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: 22
• Current Age: 32
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1092.52
• Present Value Future Benefits (PVFB): $58858.17
• Present Value Future Premiums (PVFP): $24800.62

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $34928.76
• Per $1,000 Face: $349.29

PROSPECTIVE METHOD:
• A₁_32:10⌉ = 0.2033
• ä_32:10⌉ = 8.1869
• ₁₀V = 100,000 × A₁ - P × ä = $34928.76

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10647.93
• Accumulated Cost of Insurance: $5767.32
• Interest Earned: $1541.08
• ₁₀V = $34928.76

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $33182.32
• Tax Reserve: $32134.46
• GAAP Reserve: $36675.20

Human: Calculate policy reserve for 32 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: 22
• Current Age: 32
• Policy Year: 10
• Valuation Method: Net Level Premium (NLP)

RESERVE COMPONENTS:
• Net Level Premium (P): $1092.52
• Present Value Future Benefits (PVFB): $58858.17
• Present Value Future Premiums (PVFP): $24800.62

TERMINAL RESERVE (₁₀V):
• Formula: ₁₀V = PVFB - PVFP
• Calculation: $34928.76
• Per $1,000 Face: $349.29

PROSPECTIVE METHOD:
• A₁_32:10⌉ = 0.2033
• ä_32:10⌉ = 8.1869
• ₁₀V = 100,000 × A₁ - P × ä = $34928.76

RETROSPECTIVE METHOD:
• Accumulated Premiums: $10647.93
• Accumulated Cost of Insurance: $5767.32
• Interest Earned: $1541.08
• ₁₀V = $34928.76

STATUTORY REQUIREMENTS:
• Minimum Reserve (CRVM): $33182.32
• Tax Reserve: $32134.46
• GAAP Reserve: $36675.20


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

Response:
OCCUPATIONAL MORTALITY ANALYSIS

Industry: Agriculture
Fatal Injury Rate: 49.8 per 100,000 full-time workers
Annual Deaths: 4,878

LEADING CAUSES:
• Falls: 30%
• Struck by object: 25%
• Electrocution: 6%
• Caught-in/between: 11%

Workers' compensation death benefit: $309,473

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

Actuarial AI: OCCUPATIONAL MORTALITY ANALYSIS

Industry: Agriculture
Fatal Injury Rate: 49.8 per 100,000 full-time workers
Annual Deaths: 4,878

LEADING CAUSES:
• Falls: 30%
• Struck by object: 25%
• Electrocution: 6%
• Caught-in/between: 11%

Workers' compensation death benefit: $309,473


Instruction: Calculate mortality improvement factors for age 79

Response:
MORTALITY IMPROVEMENT ANALYSIS

Age: 79
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.78%
• Current (2024): 1.75%
• Ultimate (2044+): 0.74%

PROJECTION FACTORS:
• 10-Year Factor: 0.8380
• 20-Year Factor: 0.7023
• 30-Year Factor: 0.5885

Cohort effect adjustment: Applied
Gender-specific: No

Human: Calculate mortality improvement factors for age 79

Actuarial AI: MORTALITY IMPROVEMENT ANALYSIS

Age: 79
Base Year: 2024
Improvement Scale: MP-2021

ANNUAL IMPROVEMENT RATES:
• Historical (2000-2020): 1.78%
• Current (2024): 1.75%
• Ultimate (2044+): 0.74%

PROJECTION FACTORS:
• 10-Year Factor: 0.8380
• 20-Year Factor: 0.7023
• 30-Year Factor: 0.5885

Cohort effect adjustment: Applied
Gender-specific: No