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...

In a bonus-malus system in car insurance, the bonus class of a customer is updated from one year to the next as a function of the current class and the number of claims in the year (assumed Poisson). Thus the sequence of classes of a customer in consecutive years forms a Markov chain, and most...