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.

Asymptotic distribution theory (msc 62E20), Applications to actuarial sciences and financial mathematics (msc 62P05), Central limit and other weak theorems (msc 60F05)
CWI. Probability, Networks and Algorithms [PNA]

Helmers, R, & Tarigan, B. (2003). Compound sums and their applications in finance. CWI. Probability, Networks and Algorithms [PNA]. CWI.