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On finite-time ruin probabilities for classical risk models

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  • Claude Lefèvre
  • Stéphane Loisel

Abstract

This paper examines the problem of ruin in the classical compound binomial and compound Poisson risk models. Our primary purpose is to extend to those models an exact formula derived by Picard & Lefèvre (1997) for the probability of (non-)ruin within finite time. First, a standard method based on the ballot theorem and an argument of Seal-type provides an initial (known) formula for that probability. Then, a concept of pseudo-distributions for the cumulated claim amounts, combined with some simple implications of the ballot theorem, leads to the desired formula. Two expressions for the (non-)ruin probability over an infinite horizon are also deduced as corollaries. Finally, an illustration within the framework of Solvency II is briefly presented.

Suggested Citation

  • Claude Lefèvre & Stéphane Loisel, 2008. "On finite-time ruin probabilities for classical risk models," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2008(1), pages 41-60.
    • Handle: RePEc:taf:sactxx:v:2008:y:2008:i:1:p:41-60
    DOI: 10.1080/03461230701766882
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    Cited by:

    1. Denuit, Michel & Robert, Christian Y., 2023. "Conditional mean risk sharing of losses at occurrence time in the compound Poisson surplus model," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 23-32.

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