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Extremes in Non-Life Insurance

In: Extreme Value Theory and Applications

Author

Listed:
  • Jan Beirlant

    (Katholieke Universiteit Leuven)

  • Jozef L. Teugels

    (Katholieke Universiteit Leuven)

  • Petra Vynckier

    (Katholieke Universiteit Leuven)

Abstract

We survey the impact of extreme value theory within the framework of non-life insurance. Actuaries normally have an adequate training in standard statistical techniques related to the average behaviour within a portfolio. However a rather substantial part of these portfolio’s is contaminated by claims that should be considered extreme rather than average. As a result these elements should be treated by extreme value theory rather than by central limit theory. Extreme value theory has its impact in the modeling of the claim sizes, the interclaim times and the total claim amount.Further on the ruin- probabilities both in finite and in infinite time. Probably the whole area of reinsurance is by far the most important field of application of extreme value theory since reinsurance is most often taken to safeguard the insurance company against excessive claims that may jeopardize the solvency of the company. While insurance mathematics is our prime domain of application of extreme value theory, most of the methodological results can be applied to a variety of other fields. By way of example we include an application to wind data that have previously been studied i. a. by the scholars at NIST.

Suggested Citation

  • Jan Beirlant & Jozef L. Teugels & Petra Vynckier, 1994. "Extremes in Non-Life Insurance," Springer Books, in: Janos Galambos & James Lechner & Emil Simiu (ed.), Extreme Value Theory and Applications, pages 489-510, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-3638-9_30
    DOI: 10.1007/978-1-4613-3638-9_30
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