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Modern Problems in Insurance Mathematics pp 21–36Cite as

A Note on Gerber–Shiu Functions with an Application

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Abstract

We consider a classical compound Poisson risk model. The Laplace transform of the non-discounted penalty function (also called the Gerber–Shiu function) is inverted, giving an explicit formula. By a change of measure, we can also generalise the result to discounted penalty functions. We apply this formula to obtain the value of the discounted capital injections. Finally, the asymptotic behaviour of the value of the capital injections is derived as the initial capital tends to infinity. The light and heavy tailed case, as well as some intermediate cases, are discussed.

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Author information

Authors and Affiliations

  1. University of Cologne, Cologne, Germany

    Hanspeter Schmidli

Authors
  1. Hanspeter Schmidli
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Correspondence to Hanspeter Schmidli .

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Editors and Affiliations

  1. Department of Mathematics Professor of Mathematical Statistics, Stockholm University, Stockholm, Sweden

    Dmitrii Silvestrov

  2. Department of Mathematics Professor in Mathematical Statistics, Stockholm University, Stockholm, Sweden

    Anders Martin-Löf

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Schmidli, H. (2014). A Note on Gerber–Shiu Functions with an Application. In: Silvestrov, D., Martin-Löf, A. (eds) Modern Problems in Insurance Mathematics. EAA Series. Springer, Cham. https://doi.org/10.1007/978-3-319-06653-0_4

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