8.29 A group life insurance policy has an accidental death rider. For ordinary deaths, the benefit is 10,000; however, for accidental deaths, the benefit is 20,000. The insureds are approximately the same age, so it is reasonable to assume they all have the same claim probabilities. Let them be 0.97 for no claim, 0.01 for an ordinary death claim, and 0.02 for an accidental death claim. A reinsurer has been asked to bid on providing an excess reinsurance that will pay 10,000 for each accidental death.

(a) The claim process can be modeled with a frequency component that has the Bernoulli distribution (the event is claim/no claim) and a two-point severity com­ ponent (the probabilities are associated with the two claim levels, given that a claim occurred). Specify the probability distributions for the frequency and sever­ ity random variables.

(b) Suppose the reinsurer wants to retain the same frequency distribution. Deteanine the modified severity distribution that will reflect the reinsurer's payments.

(c) Determine the reinsurer' s frequency and severity distributions when the severity distribution is to be conditional on a reinsurance payment being made.