On Finite-Time Ruin Probabilities for Classical Risk Models

Claude Lefèvre () and Stéphane Loisel
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Claude Lefèvre: ULB - Département de Mathématique [Bruxelles] - ULB - Faculté des Sciences [Bruxelles] - ULB - Université libre de Bruxelles

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Abstract: This paper is concerned with 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 and 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.

Keywords: Value-at-Risk; ruin probability; finite and infinite horizon; compound binomial model; compound Poisson model; ballot theorem; pseudo-distributions; Solvency II; Value-at-Risk. (search for similar items in EconPapers)
Date: 2008-01
Note: View the original document on HAL open archive server: https://hal.science/hal-00168958v1
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Citations: View citations in EconPapers (23)

Published in Scandinavian Actuarial Journal, 2008, 2008 (1), pp.41-60. ⟨10.1080/03461230701766882⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00168958

DOI: 10.1080/03461230701766882

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