Random number generators for compound distributions

Abstract

Abstract Modem digital computers have made it possible to apply more complex models for stochastic phenomena by using random number simulation when it would be impossible, or impractical, to construct and explicitly solve equations describing the phenomena in question. Compound random variables often play a central role in insurance risk processes. A well-known difficulty in generating random numbers with a compound distribution is that, in order to make them accurate enough, the computer time needed tends to grow too much. In this paper a random number generator for compound distributions is introduced, which is, in principle, exact or highly accurate for a wide class of distributions of the size of one claim, and yet generates random numbers in a rate essentially independent of the number of claims.