Final answer:
The calculation of actuarially fair premiums in life insurance takes into account the risk of death within a specified time frame. If sold separately to groups with different risks, premiums would differ. Charging a single average premium for all may result in adverse selection, posing a risk to the insurance company.
Step-by-step explanation:
The question seems to address aspects of cash-value whole life insurance and the calculation of actuarially fair premiums. In this scenario, we are given two groups of 50-year-old men differentiated by their family history of cancer, which affects their mortality risk. If insurance is sold separately, premiums would be set according to each group's risk. Group one with a family history has a higher risk of 1 in 50 of dying in the next year. Group two without a history has a lower risk of 1 in 200 of dying in the next year. Premiums are calculated by the expected payout which equals the probability of the event (death) multiplied by the amount of the benefit (death benefit).
For group one, the actuarially fair premium would be (1/50) * $100,000, and for group two, it would be (1/200) * $100,000. If the insurer cannot differentiate between groups and charges an average premium to all, the premium for low-risk individuals might be seen as too high, resulting in adverse selection where higher risk individuals are more likely to buy insurance while lower risk ones opt out. This imbalance could lead to an unsustainable insurance pool.
The insurer faces a risk of adverse selection if it charges an average premium to the entire group. By doing so, it may attract a disproportionate number of high-risk individuals, as those with lower risks may not find the premium favorable. This situation can adversely affect the sustainability of the insurance company's funds since premiums collected may not cover the payouts for the higher overall risk.