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Some Remarks on Delayed Renewal Risk Models

Published online by Cambridge University Press:  09 August 2013

Jae-Kyung Woo
Jae-Kyung Woo*
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, Canada, E-mail: [email protected]
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Abstract

Some extensions to the delayed renewal risk models are considered. In particular, the independence assumption between the interclaim time and the subsequent claim size is relaxed, and the classical Gerber-Shiu penalty function is generalized by incorporating more variables. As a result, general structures regarding various joint densities of ruin related quantities as well as their probabilistic interpretations are provided. The numerical example in case of time-dependent claim sizes is provided, and also the usual delayed model with time-independent claim sizes is discussed including a special case with exponential claim sizes. Furthermore, asymptotic formulas for the associated compound geometric tail for the present model are derived using two alternative methods.

Keywords

Delayed renewal risk modelGerber-Shiu functionLast ladder heightLast interclaim timeCramer's asymptotic ruin formula
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 1 , May 2010 , pp. 199 - 219
Copyright
Copyright © International Actuarial Association 2010

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