中文摘要：

本文讨论了索赔到达过程为一般Markov点过程,即考虑索赔到达为MAP过程的一类带干扰的风险模型,给出了期望贴现惩罚函数的Laplace变换满足的积分-微分方程,对于Laplace变换为有理函数的索赔分布,采用差分变换方法,利用Dickson-Hipp算子,本文得到了期望贴现惩罚函数的简洁表达式。

英文摘要：

A risk model perturbed by diffusion is proposed in this paper.Claims arrival belongs to markovian arrival process（MAP）.The integro-differential equations satisfied by Laplace transform of the Gerber-Shiu functions and closed form of expression for the Gerber-Shiu functions are obtained through divided difference and Dickson-Hipp operator when the claim amount distribution is from the rational family.Finally,in order to illustrate the main results,a numerical example is provided.