Consider a simple loss process where the number of claims follows a Poisson distribution with rate λ = 5 and the individual claim amount follows a lognormal distribution with µ = 11 and σ = 2.

Assume that the insurer offers a simple stop loss protection by which the insurer pays all losses in excess of an aggregate yearly amount of AAD = £ . 2 5M. (In mathematical terms, if S is the annual loss amount, the amount paid by the insurer is Sced = − max(0,S AAD).

Using Monte Carlo simulation, estimate the earning pattern resulting from this situation, and explain why it differs from a uniform distribution.