Question

Consider a five-year term insurance issued to a select life aged 40 by a single premium, with sum insured $1 million payable immediately on death. Assume that mortality follows the standard select life table, with UDD between integer ages, and assume an interest rate of 5% per year.

a. Calculate the premium for the insurance policy.
b. Assess the impact of changing interest rates on the policy's cost.
c. Analyze the financial implications of different sum insured values.
d. Examine the role of mortality tables in insurance pricing.

Answer 1

a. The actuarially fair premium for the group with a family history of cancer would be $20,000, and for the group without a family history of cancer it would be $80,000. b. 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 $80,000. c. Charging the actuarially fair premium to the group as a whole instead of each group separately could result in adverse selection.

Step-by-step explanation:

a. To calculate the actuarially fair premium for each group, we need to consider the expected value of the payout for each group. For the group with a family history of cancer, there is a 20% chance of dying in the next year with a payout of $100,000. So the expected payout is $100,000 * 0.2 = $20,000. For the group without a family history of cancer, there is an 80% chance of dying in the next year with a payout of $100,000. So the expected payout is $100,000 * 0.8 = $80,000. Therefore, the actuarially fair premium for each group would be equal to their expected payout, so $20,000 for the group with a family history of cancer and $80,000 for the group without a family history of cancer.

b. 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 calculated by taking the weighted average of the expected payouts for each group. The weight would be based on the proportion of individuals in each group. In this case, 20% of the group has a family history of cancer and 80% does not. So the actuarially fair premium for the group as a whole would be (0.2 * $20,000) + (0.8 * $80,000) = $16,000 + $64,000 = $80,000.

c. If the insurance company tries to charge the actuarially fair premium to the group as a whole rather than to each group separately, it would be charging the same premium to individuals with different risk profiles. Individuals with a family history of cancer would be paying more than their expected payout, while those without a family history of cancer would be paying less than their expected payout. This could lead to adverse selection, where individuals with a higher risk are more likely to purchase the insurance, resulting in losses for the insurance company.