Compound Sums and Their Applications in Finance

R. Helmers, B. Tarigan

Data & Software Engineering Research Group
STEI-ITB, Jl. Ganeca No.10, Bandung 40132, Indonesia

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 perform very badly, one may look for better methods for approximating the distribution of compound sum, e.g. the bootstrap or 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 ruin in the Poisson risk model, for the special case where the claim sizes are assumed to be exponentially distributed.

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