We show how, from a single simulation run, to estimate the ruin probabilities and their sensitivities (derivatives) in a classic insurance risk model under various distributions of the number of claims and the claim size. Similar analysis is given for the tail probabilities of the accumulated...

Importance sampling is one of the classical variance reduction techniques for increasing the efficiency of Monte Carlo algorithms for estimating integrals. The basic idea is to replace the original random mechanism in the simulation by a new one and at the same time modify the function being...