On a class of renewal risk model with random income

Hu Yang and Zhimin Zhang

Applied Stochastic Models in Business and Industry, 2009, vol. 25, issue 6, 678-695

Abstract: In this paper, we consider a renewal risk process with random premium income based on a Poisson process. Generating function for the discounted penalty function is obtained. We show that the discounted penalty function satisfies a defective renewal equation and the corresponding explicit expression can be obtained via a compound geometric tail. Finally, we consider the Laplace transform of the time to ruin, and derive the closed‐form expression for it when the claims have a discrete Km distribution (i.e. the generating function of the distribution function is a ratio of two polynomials of order m∈ℕ+). Copyright © 2008 John Wiley & Sons, Ltd.

Date: 2009
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https://doi.org/10.1002/asmb.752

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Persistent link: https://EconPapers.repec.org/RePEc:wly:apsmbi:v:25:y:2009:i:6:p:678-695

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