The expectation of aggregate discounted dividends for a Sparre Anderson risk process perturbed by diffusion

Hui Meng, Chunsheng Zhang and Rong Wu

Applied Stochastic Models in Business and Industry, 2007, vol. 23, issue 4, 273-291

Abstract: In this paper, we study the expectation of aggregate dividends until ruin for a Sparre Andersen risk process perturbed by diffusion under a threshold strategy, in which claim waiting times have a common generalized Erlang(n) distribution. For this strategy, we assume that if the surplus is above certain threshold level before ruin, dividends are continuously paid at a constant rate that does not exceed the premium rate, and if not, no dividends are paid. We obtain some integro‐differential equations satisfied by the expected discounted dividends, and further its renewal equations. Finally, applying these results to the Erlang(2) risk model perturbed by diffusion, where claims have a common exponential distributions, we give some explicit expressions and numerical analysis. Copyright © 2007 John Wiley & Sons, Ltd.

Date: 2007
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https://doi.org/10.1002/asmb.670

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Persistent link: https://EconPapers.repec.org/RePEc:wly:apsmbi:v:23:y:2007:i:4:p:273-291

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