Question

An insurer has discovered a misrepresentation on a life insurance policy application regarding the insured's age. The insured is 10 years older than he stated on the application. What will the insurer do regarding the death benefit?

Answer 1

If the insurance company were selling life insurance separately to each group, 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 would be $80,000. If the insurance company were offering life insurance to the entire group without knowing their family cancer histories, the actuarially fair premium for the group as a whole would be $64,000. Charging the actuarially fair premium to the group as a whole instead of separately to each group may result in 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 by multiplying the probability of dying in the next year by the payout amount of $100,000. For the group with a family history of cancer, 20% of the 1,000 men would be 200 men. The probability of dying for this group is 1 in 50, so the actuarially fair premium would be (200/1000) * $100,000 = $20,000. For the group without a family history of cancer, 80% of the 1,000 men would be 800 men. The probability of dying for this group is 1 in 200, so the actuarially fair premium would be (800/1000) * $100,000 = $80,000.

If the insurance company were offering life insurance to the entire group without knowing their family cancer histories, the actuarially fair premium for the group as a whole can be calculated by taking a weighted average of the premiums for each group based on their probabilities of having a family history of cancer. The probability of having a family history of cancer is 20%, so the actuarially fair premium would be (0.2 * $20,000) + (0.8 * $80,000) = $64,000.

If the insurance company tries to charge the actuarially fair premium to the group as a whole instead of separately to each group, it may face adverse selection. Adverse selection occurs when the group with a higher probability of needing the insurance ends up paying less for it compared to the lower-risk group. This can result in financial losses for the insurance company if the premium collected is insufficient to cover the claims made by the higher-risk group.