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Gerber–Shiu analysis with a generalized penalty function

Author

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  • Eric Cheung
  • David Landriault
  • Gordon Willmot
  • Jae-Kyung Woo

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.

Suggested Citation

  • Eric Cheung & David Landriault & Gordon Willmot & Jae-Kyung Woo, 2010. "Gerber–Shiu analysis with a generalized penalty function," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2010(3), pages 185-199.
    • Handle: RePEc:taf:sactxx:v:2010:y:2010:i:3:p:185-199
    DOI: 10.1080/03461230902884013
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    Cited by:

    1. Tao Sun & Xinqiu Zhang, 2024. "Laplace Transformation of the Ruin Time for a Risk Model with a Parisian Implementation Delay," Mathematics, MDPI, vol. 12(4), pages 1-12, February.
    2. Cheung, Eric C.K., 2011. "A generalized penalty function in Sparre Andersen risk models with surplus-dependent premium," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 384-397, May.

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