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The perturbed compound Poisson risk model with linear dividend barrier

✍ Scribed by Donghai Liu; Zaiming Liu

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
227 KB
Volume
235
Category
Article
ISSN
0377-0427

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✦ Synopsis

In this paper, we consider a diffusion perturbed classical compound Poisson risk model in the presence of a linear dividend barrier. Partial integro-differential equations for the moment generating function and the nth moment of the present value of all dividends until ruin are derived. Moreover, explicit solutions for the nth moment of the present value of dividend payments are obtained when the individual claim size distribution is exponential. We also provided some numerical examples to illustrate the applications of the explicit solutions. Finally we derive partial integro-differential equations with boundary conditions for the Gerber-Shiu function.

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