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Methodology and Computing in Applied Probability

, Volume 11, Issue 3, pp 425–441 | Cite as

Finite-Time Ruin Probabilities for Discrete, Possibly Dependent, Claim Severities

  • Claude LefèvreEmail author
  • Stéphane Loisel
Article

Abstract

An important question in insurance is how to evaluate the probabilities of (non-) ruin of a company over any given horizon of finite length. This paper aims to present some (not all) useful methods that have been proposed so far for computing, or approximating, these probabilities in the case of discrete claim severities. The starting model is the classical compound Poisson risk model with constant premium and independent and identically distributed claim severities. Two generalized versions of the model are then examined. The former incorporates a non-constant premium function and a non-stationary claim process. The latter takes into account a possible interdependence between the successive claim severities. Special attention will be paid to a recursive computational method that enables us to tackle, in a simple and unified way, the different models under consideration. The approach, still relatively little known, relies on the use of remarkable families of polynomials which are of Appell or generalized Appell (Sheffer) types. The case with dependent claim severities will be revisited accordingly.

Keywords

Ruin probability Finite-time horizon Compound Poisson risk model Non-constant premium Non-stationary claim arrivals Interdependent claim severities Recursive computational methods Appell polynomials Generalized Appell (Sheffer) polynomials 

AMS 2000 Subject Classification

62P05 60G40 12E05 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Département de MathématiqueUniversité Libre de BruxellesBruxellesBelgium
  2. 2.Institut de Science Financière et d’AssurancesUniversité de LyonLyonFrance

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