Determining the total loss distribution from the moments of the exponential of the compound loss

Henryk Gzyl

Journal of Operational Risk

Abstract: ABSTRACT An important problem in the field of insurance and operational risk is the determination of the distribution function when a compound loss model is used for the total loss. A large variety of methods have been developed for this purpose. Here we explore some mathematical aspects of a method consisting of the reconstruction of the cumulative distribution function or the probability density of the compound loss, based on the knowledge of the Laplace transform of the compound loss, or, equivalently, based on the knowledge of the moments of the exponential of the compound loss. This is particularly useful when analytical models exist for the individual severities and for the frequency of events. In this case the moments are the values of the Laplace transform of the compound severity at integer points.

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