一类带干扰稀疏风险模型红利付款现值的研究

On Discounted Dividend Payments in Thinning Risk Model Perturbed by Diffusion

对常数红利边界策略下带干扰的稀疏风险模型进行研究,其中保费收入过程为一复合Poisson过程,而索赔计数过程是保单到达过程的p-稀疏过程.得到了直至破产时红利付款现值的期望、矩母函数和n阶矩所满足的积分—微分方程及边界条件.

In this paper ,the perturbed risk model with a constant dividend barrier strategy has been consid-ered ,in w hich the aggregate premium process is a compound Poisson process and the claim number process is a p-thinning process of the premium arriving number process .The integral-differential equations with boundary conditions for the expectation ,the moment generating function and the n the moment of the dis-counted dividend payments until ruin are obtained .