Compound sums and their applications in finance

Compound sums arise frequently in insurance (total claim size in a portfolio) and in accountancy (total error amount in audit populations). As the normal approximation for compound sums usually performs very badly, one may look for better methods for approximating the distribution of a compound sum, e.g. the bootstrap or empirical Edgeworth/saddlepoint approximations. We sketch some recent developments and indicate their relevance in finance. Second, we propose and investigate a simple estimator of the probability of ruin in the Poisson risk model, for the special case where the claim sizes are assumed to be exponentially distributed.