Gerber–Shiu analysis with a generalized penalty function

Eric Cheung, David Landriault, Gordon Willmot and Jae-Kyung Woo

Scandinavian Actuarial Journal, 2010, vol. 2010, issue 3, 185-199

Abstract: A generalization of the usual penalty function is proposed, and a defective renewal equation is derived for the Gerber–Shiu discounted penalty function in the classical risk model. This is used to derive the trivariate distribution of the deficit at ruin, the surplus prior to ruin, and the surplus immediately following the second last claim before ruin. The marginal distribution of the last interclaim time before ruin is derived and studied, and its joint distribution with the claim causing ruin is derived.

Date: 2010
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DOI: 10.1080/03461230902884013

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