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On a general class of renewal risk process: analysis of the Gerber-Shiu function

Part of: Applications Special processes

Published online by Cambridge University Press:  01 July 2016

Shuanming Li  and
José Garrido
Shuanming Li*
Affiliation:
University of Melbourne
José Garrido*
Affiliation:
Concordia University
*
∗ Postal address: Centre for Actuarial Studies, University of Melbourne, Victoria 3010, Australia.
∗∗ Postal address: Department of Mathematics and Statistics, Concordia University, Montreal, Quebec H4B 1R6, Canada. Email address: [email protected]
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Abstract

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We consider a compound renewal (Sparre Andersen) risk process with interclaim times that have a Kn distribution (i.e. the Laplace transform of their density function is a ratio of two polynomials of degree at most n ∈ N). The Laplace transform of the expected discounted penalty function at ruin is derived. This leads to a generalization of the defective renewal equations given by Willmot (1999) and Gerber and Shiu (2005). Finally, explicit results are given for rationally distributed claim severities.

Keywords

Sparre Andersen risk processKn family of distributionsmartingaleLaplace transformgeneralized Lundberg equationdefective renewal equation

MSC classification

Primary: 62P05: Applications to actuarial sciences and financial mathematics
Secondary: 60K05: Renewal theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 37 , Issue 3 , September 2005 , pp. 836 - 856
Copyright
Copyright © Applied Probability Trust 2005 

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