Homework Assignment 22: (1) Do Exercise 14.5 on page 462. (In part (b), the “first method” refers to the approximation we developed in class.) (2) Consider a group life insurance contract with an accidental death benefit. Assume that for all members the probability of death in the next year is .01 and that 30% of the deaths are accidental. For 50 employees the benefit for an ordinary death is 50,000 and for an accidental death it is 100,000. For the remaining 25 employees the benefits are 75,000 and 150,000. What compound Poisson distribution would be used for approximating the individual model? (Ans λ = 0.75, p(50,000) = 0.4667, p(75,000) = 0.2333, p(100,000) = 0.2000, p(150,000) = 0.1000) (3) An life insurance company has a portfolio of independent risks as shown below: Class Probability of a Claim Benefit Number of Policies 1 0.1 1 100 2 0.2 2 100 3 0.5 2 100 X is the variance of aggregate claims using the individual model. Y is the variance of aggregate claims using the compound Poisson approximation,
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Probability theory, compound Poisson, individual model, compound Poisson approximation