Final answer:
The subject of this question is Business and it asks about the actuarially fair premium for different groups and the consequences of charging the premium to the group as a whole.
Step-by-step explanation:
The subject of this question is Business. The question is asking about the actuarially fair premium for each group if the insurance company were selling life insurance separately to each group, the actuarially fair premium for the group as a whole if the company could not find out about family cancer histories, and what will happen to the insurance company if it tries to charge the actuarially fair premium to the group as a whole rather than to each group separately. The question involves calculating the actuarially fair premium for life insurance policies based on varying degrees of risk due to family cancer history. To answer part (a), we distinguish between two groups within a population of 1,000 50-year-old men. For the 20% with a family history, the fair premium is calculated by multiplying the probability of death (1/50) by the insurance payout ($100,000).
Conversely, for the 80% without a family history, we multiply their lower probability of death (1/200) by the same insurance payout. Part (b) requires an average premium calculation that takes into account the combined risk. For part (c), if the company charges the actuarially fair premium for the entire group without considering individual risks, it may find the premium inadequate for those with higher risks, causing financial imbalance.Actuarially fair premiums are crucial for insurance companies in maintaining financial stability and managing risk. Charging premiums based on averaged risks, without separating individuals into accurate risk groups, can lead to adverse selection, where individuals with high risk are subsidized by those with lower risks, potentially leading to financial losses for the company over time.