Problem 7.4.

(10 pts) In the compound model for aggregate claims, let the frequency random Variable N have the geometric distribution with mean 4. Moreover, let the individual losses have the distribution pX(0) = , pX(100) = 1/2. Define the aggregate loss as S=N j=1, Xj.How much is E[(S100)+]?

Problem 7.5

In the compound model for aggregate claims, let the frequency random variable N be negative binomial with parameters r= 15 and = 5. Moreover, let the common distribution of the i.i.d.severity random variables {Xj;j=1,2,...} be the two-parameter Pareto with = 3 and = 10. Let our usual assumptions hold, i.e., let N be independent of {Xj;j= 1,2,...}. The insurer is interested in finding the total premium such that the aggregate losses exceed it with the probability less than or equal to 5%. Using the normal approximation, find such that P[S > ] = 0.05.