The expectation of aggregate discounted dividends for a Sparre Anderson risk process perturbed by diffusion
The expectation of aggregate discounted dividends for a Sparre Anderson risk process perturbed by diffusion
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DOI：
10.1002/asmb.670
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发表时间：
2007-07
影响因子：
1.4
通讯作者：
Hui Meng;Chunsheng Zhang;R. Wu
中科院分区：
文献类型：
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作者：
Hui Meng;Chunsheng Zhang;R. Wu
本文研究了一类受扩散干扰的Sparre Andersen风险过程在阈值策略下破产前的总红利期望，其中索赔等待时间服从共同的广义Erlang(N)分布。对于这一策略，我们假设如果破产前盈余高于某个阈值水平，则以不超过保费的恒定比率连续支付红利，如果不超过，则不支付红利。得到了期望贴现股利满足的积分-微分方程组，并进一步得到了它的更新方程。最后，将这些结果应用于索赔服从共同指数分布的受扩散干扰的Erlang(2)风险模型，给出了一些显式表达式和数值分析。版权所有©2007 John Wiley&Sons，Ltd.
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.