Final answer:
The question involves business and insurance concepts, particularly life insurance premium calculations based on risk factors. An actuarially fair premium must be calculated based on the probability of deaths in different risk groups, with $100,000 being the payout for each death. Not adjusting premiums for varying risk can lead to adverse selection, which threatens the insurance company's financial balance.
Step-by-step explanation:
If a client chooses a variable life insurance plan with a guaranteed minimum death benefit, the plan will offer both a death benefit and a cash value component. The cash value accumulates over time and can be used by the policyholder.
For an insurance company to determine an actuarially fair premium, especially in scenarios where clients have different risk profiles, such as a family history of cancer, it must calculate the likelihood of a payout as well as the expected value of such payouts.
To find the actuarially fair premium for each risk group:
- For the group with a family history of cancer (20% of 1,000 men): 20 men (1 chance in 50 of dying) will yield roughly 0.4 expected deaths. At $100,000 per death, this group would contribute $40,000 to the risk pool.
- For the group without a family history of cancer (80% of 1,000 men): 80 men (1 chance in 200 of dying) will yield 0.4 expected deaths. This group would also contribute $40,000 to the risk pool.
- The combined expected deaths are 0.8, and the combined contribution is $80,000. Therefore, the fair premium per person would be $80, which is the total risk pool divided by the number of insured individuals (1,000).
If the insurance company charges the actuarially fair premium to the entire group without considering family cancer histories, they would need to charge each individual the same amount, $80. However, if they charged this amount, the healthier group is subsidizing the higher-risk group, which might lead to adverse selection.
If an insurance company charges an actuarially fair premium separately to each group, it will ensure that each group pays in proportion to their risk level.
Failing to differentiate between the two groups may result in the healthier group being overcharged, potentially driving them away from purchasing insurance from the company, a phenomenon known as adverse selection.