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Direct Derivation of Finite-Time Ruin Probabilities in the Discrete Risk Model with Exponential or Geometric Claims

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  • Wai-Sum Chan
  • Lianzeng Zhang

Abstract

Growing research interest has been shown in finite-time ruin probabilities for discrete risk processes, even though the literature is not as extensive as for continuous-time models. The general approach is through the so-called Gerber-Shiu discounted penalty function, obtained for large families of claim severities and discrete risk models. This paper proposes another approach to deriving recursive and explicit formulas for finite-time ruin probabilities with exponential or geometric claim severities. The proposed method, as compared to the general Gerber-Shiu approach, is able to provide simpler derivation and straightforward expressions for these two special families of claims.

Suggested Citation

  • Wai-Sum Chan & Lianzeng Zhang, 2006. "Direct Derivation of Finite-Time Ruin Probabilities in the Discrete Risk Model with Exponential or Geometric Claims," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(4), pages 269-279.
    • Handle: RePEc:taf:uaajxx:v:10:y:2006:i:4:p:269-279
    DOI: 10.1080/10920277.2006.10597426
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    Cited by:

    1. Ekaterina Bulinskaya & Boris Shigida, 2021. "Discrete-Time Model of Company Capital Dynamics with Investment of a Certain Part of Surplus in a Non-Risky Asset for a Fixed Period," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 103-121, March.
    2. Ekaterina Bulinskaya & Julia Gusak & Anastasia Muromskaya, 2015. "Discrete-time Insurance Model with Capital Injections and Reinsurance," Methodology and Computing in Applied Probability, Springer, vol. 17(4), pages 899-914, December.
    3. Landriault, David & Shi, Tianxiang & Willmot, Gordon E., 2011. "Joint densities involving the time to ruin in the Sparre Andersen risk model under exponential assumptions," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 371-379.

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