The distribution of the dividend payments in the compound poisson risk model perturbed by diffusion
The distribution of the dividend payments in the compound poisson risk model perturbed by diffusion
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DOI：
10.1080/03461230600589237
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发表时间：
2006-03
影响因子：
1.8
通讯作者：
Shuanming Li
中科院分区：
文献类型：
--
作者：
Shuanming Li
考虑了一类带扩散扰动的经典复合Poisson风险模型，该模型具有一个常数红利边界。建立了破产前股利折现支付的n阶矩满足一定边界条件的积分微分方程，并求解了该方程。它的解可以表示为相应的无障碍扰动风险模型中由于振动引起的期望罚金折现（Gerber-Shiu）函数。当贴现因子δ为零时，证明了在无障碍扰动风险模型中，所有结果都可用非破产概率表示.
We consider a diffusion perturbed classical compound Poisson risk model in the presence of a constant dividend barrier. An integro-differential equation with certain boundary conditions for the n-th moment of the discounted dividend payments prior to ruin is derived and solved. Its solution can be expressed in terms of the expected discounted penalty (Gerber-Shiu) functions due to oscillation in the corresponding perturbed risk model without a barrier. When the discount factor δ is zero, we show that all the results can be expressed in terms of the non-ruin probability in the perturbed risk model without a barrier.