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Exponential Behavior in the Presence of Dependence in Risk Theory

Part of: Stochastic processes Special processes Applications

Published online by Cambridge University Press:  14 July 2016

Hansjörg Albrecher  and
Jef L. Teugels
Hansjörg Albrecher*
Affiliation:
Austrian Academy of Sciences, Linz, and Graz University of Technology
Jef L. Teugels*
Affiliation:
Katholieke Universiteit Leuven and EURANDOM
*
∗ Postal address: Department of Mathematics, Graz University of Technology, Steyrergasse 30, Graz, 8010, Austria. Email address: albrecher@tugraz.at
∗∗ Postal address: Department of Mathematics, Katholieke Universiteit Leuven, de Croylaan 54, Heverlee, 3001, Belgium.
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Abstract

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We consider an insurance portfolio situation in which there is possible dependence between the waiting time for a claim and its actual size. By employing the underlying random walk structure we obtain explicit exponential estimates for infinite- and finite-time ruin probabilities in the case of light-tailed claim sizes. The results are illustrated in several examples, worked out for specific dependence structures.

Keywords

Dependencerisk modelcopularenewal theoryWiener-Hopf theory

MSC classification

Primary: 62P05: Applications to actuarial sciences and financial mathematics
Secondary: 60G50: Sums of independent random variables; random walks 60K05: Renewal theory

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 1 , March 2006 , pp. 257 - 273
Copyright
© Applied Probability Trust 2006 

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