Direct Derivation Of Finite-Time Ruin Probabilities In The Discrete Risk Model With Exponential Or Geometric Claims

North American Actuarial Journal
Volume 10, Issue 4, 2006
Wai-Sum Chan FSA, PhD & Lianzeng Zhang PhD

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.

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