Question

a life insurer is about to issue a 30-year deferred annuity-due with annual payments of $20 000 to a select life aged 35. the policy has a single premium which is refunded without interest at the end of the year of death if death occurs during the deferred period. assume that mortality follows the standard select life table, and that the interest rate is 5% per year.

Answer 1

The actuarially fair premium for each group can be calculated by considering the mortality rates and expected payouts for the two groups separately. If the insurance company can't determine the family cancer history, the actuarially fair premium for the group as a whole would be a weighted average of the premiums for each group. Charging the actuarially fair premium to the group as a whole instead of separately could lead to adverse selection.

Step-by-step explanation:

If the insurance company were selling life insurance separately to each group, the actuarially fair premium for each group can be calculated as follows:

For the group with a family history of cancer: 20% * 1000 = 200 men

Mortality rate: 1 in 50

Expected number of deaths: 200 / 50 = 4 deaths

Expected payout: 4 * $100,000 = $400,000

Actuarially fair premium for this group: $400,000 / 200 = $2,000

For the group without a family history of cancer: 80% * 1000 = 800 men

Mortality rate: 1 in 200

Expected number of deaths: 800 / 200 = 4 deaths

Expected payout: 4 * $100,000 = $400,000

Actuarially fair premium for this group: $400,000 / 800 = $500

If the insurance company could not find out about family cancer histories and were offering life insurance to the entire group, the actuarially fair premium for the group as a whole would be the weighted average of the premiums for each group based on their population percentage. In this case, the actuarially fair premium for the group as a whole would be:

(20% * $2,000 + 80% * $500) = $260 + $400 = $660

If the insurance company tries to charge the actuarially fair premium to the group as a whole rather than to each group separately, the company may face adverse selection. Adverse selection occurs when individuals with a higher risk of death are more likely to purchase insurance. In this case, individuals with a family history of cancer would be overpaying for their premiums, while individuals without a family history of cancer would be underpaying. This imbalance in premiums could make the insurance product less attractive to the target market.