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On a class of renewal risk model with random income

✍ Scribed by Hu Yang; Zhimin Zhang

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
148 KB
Volume
25
Category
Article
ISSN
1524-1904

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✦ Synopsis

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 K~m~ distribution (i.e. the generating function of the distribution function is a ratio of two polynomials of order mβˆˆβ„•^+^). Copyright Β© 2008 John Wiley & Sons, Ltd.

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