Final answer:
The rate of premium for fire insurance policies is determined by risk assessment, with premiums designed to reflect expected losses. An actuarially fair premium ensures policyholders pay an amount equal to the expected payouts within their risk group. Without precise risk differentiation, such as in heterogeneous risk pools, adverse selection may pose a financial risk to the insurer.
Step-by-step explanation:
The rate of premium for fire insurance policies is calculated based on actuarial science, which assesses risk and uncertainty. Using the example provided, if we have two distinct groups based on their risk factors, the premium would be tailored to reflect the expected losses of each group. The rate that results in premiums equal to the sum that an average person in that risk group would collect in insurance payments is referred to as an actuarially fair premium.
For instance, considering the men with a family history of cancer, if 20% of the 1,000 men (which is 200 men) have a 1 in 50 chance of dying, that means 4 deaths are expected. At $100,000 payout per death, the total expected payout is $400,000. Thus, the actuarially fair premium would be $400,000 divided by the 200 men, amounting to $2,000 per person. For the other 80% without a family history, we expect 4 deaths (800 men with a 1 in 200 chance), so again, $400,000 in payouts, but since the group is larger, the premium per person would be $500.
This adverse selection can result in insufficient premiums to cover the payouts for high-risk individuals, potentially jeopardizing the insurance company's financial stability. Therefore, the company needs to consider various factors such as investment income, administrative costs, and need for profit to determine a premium that is fair but also ensures the company's solvency.