To assess the required capital for insurance companies, which usually have several business lines, estimates of the joint tail probabilities of aggregate losses are needed. Under the collective risk model, these aggregate losses are sums of random number of random variables, whose distributions...

This paper studies in detail simulation methods for simulating tail probability and tail mean of both univariate and bivariate compound variables. We first reviewed some basic variance reduction methods, then we proposed several novel combinations of variance reduction methods specifically for...