1. Aggregate claims from a risk have a compound Poisson distribution, with Poisson parameter 10 and the individual claim amount distribution is ex- ponential with mean 100. An insurer charges a premium of 1, 100 to cover this risk, and arranges excess of loss reinsurance with retention level d. The random variable Y denotes aggregate claims paid by the re-insurer, and if the reinsurance premium is given by E[Y] +0.001V [Y], find the reinsurance premium. 2. Aggregate claims S, from a risk have a compound Poisson distribution with Poisson parameter 50 and individual claim X amounts are distributed according to the mixed exponential distribution F(x)=1-0.4e-0.01x 0.6e - -0.02x for x > 0. Calculate approximate values of P(S 4,500) using a translated gamma approximation. 3. S has a compound negative binomial distribution with negative binomial parameter k = 80 and p = 0.4. Individual claim amounts are lognormally distributed with mean 1 and variance 1.5. Calculate E [S] and V[S].