On a class of renewal risk model with random income |
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Authors: | Hu Yang Zhimin Zhang |
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Affiliation: | Department of Statistics and Actuarial Science, Chongqing University, Chongqing 400030, People's Republic of China |
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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∈?+). Copyright © 2008 John Wiley & Sons, Ltd. |
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Keywords: | discounted penalty function generating function Km distribution the time to ruin |
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