Homework Assignment 24: (1) Aggregate claims has a compound Poisson distribution with λ = 1 and p(1) = p(2) = 0.5. For a premium of 4.0, an insurer will pay total claims and a dividend equal to the excess, if any, of 75% of the premium over 100% of the claims. Determine the expected dividend. (Ans 1.701) (2) For a certain group, aggregate claims are uniformly distributed over (0,10). Insurer A proposes stop-loss coverage with a deductible of 6 for a premium equal to the expected stop-loss claims. Insurer B proposes group coverage with a premium of 7 and a dividend equal to the excess, if any, of 7 k over claims. Calculate k such that the expected cost to the group is equal under both proposals. (Ans 0.90) (3) An insurer has an aggregate claims process that is compound Poisson with λ = 1 and p(x) = (1/4)e-x/4 , x>0. With no reinsurance, the insurer has a relative security loading of 1.25. The insurer purchases reinsurance that has expected claims of 2.
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