Final answer:
Variable whole life insurance is the policy with a fixed premium, cash value, and a fluctuating death benefit based on investment performance. An actuarially fair premium reflects the expected claims and varies with risk diversity in a group. Combining different risk groups without adjusting premiums can lead to adverse selection.
Step-by-step explanation:
The life insurance policy that has a fixed premium, a cash value, and a death benefit that can fluctuate based on investment performance is Variable whole life insurance. This type of policy combines the permanent protection of whole life insurance with investment account options, where the cash value and death benefit may vary in response to the performance of the investments chosen. Unlike the other options, such as annually renewable term insurance which does not have cash value, and variable lifetime annuity, which focuses on income streams for retirement rather than a death benefit, variable whole life is designed to be a long-term, permanent life insurance solution with an investment component.
An actuarially fair premium is one where the premium charged equals the expected payout, considering the probability and timing of a claim. For a group with family cancer history versus without, these premiums would be different due to varying risks. If they were combined into a single group without distinguishing their cancer histories, the premium will be an average that might not reflect the true risk of each subgroup, leading to adverse selection where higher-risk individuals may be more likely to purchase insurance.