Final answer:
An actuarially fair premium is based on the risk profile of the insured, and it would vary for groups with different family cancer histories. Without individual risk information, the premium would be a blended rate for the whole group. Asymmetric information affects premium calculations, as insured individuals may possess more personal risk data than the insurer.
Step-by-step explanation:
The question pertains to the actuarially fair premium for life insurance policies. An actuarially fair premium is calculated based on the risk profile of an insured group or individual which includes considering the likelihood of a claim and potential amount to be paid out. Therefore:
For each group with known family cancer histories, the actuarial fair premium would be set according to the specific risk associated with their respective histories. This would generally mean higher premiums for groups with a higher risk of cancer.
Without information on family cancer histories, the insurance company would calculate a single actuarial fair premium based on the combined risk profile of all the individuals in the group, resulting in a blended rate that accounts for the average risk of both those with and without family histories of cancer.
This method reflects the concept of asymmetric information in the insurance market, where the insured may know more about their personal risk factors, such as family health history or driving habits, than the insurer can. Consequently, the insurance company adjusts premiums to manage their risk exposure.