中文摘要：

本文研究了当保费率随时间变化时的复合Poisson-Geometric 过程的风险模型.通过无穷小方法,得到了该模型的Gerber-Shiu 折现惩罚函数所满足的更新方程.在此基础上,推导出破产概率,破产前瞬时盈余,以及破产时刻赤字分布满足的更新方程.特别地,当个体索赔服从指数分布时,通过求解微分方程,得到了该模型的破产概率的显式表达式和所满足的不等式.最后通过数值模拟和算例分析,提出了保险公司的赔付政策和保费政策对自身风险的影响.

英文摘要：

In this paper, we consider a new risk model of compound Poisson-Geometric process which assumes that the insurance company receives the premium with a differentiable rate. By applying the differential argument method, a defective renewal equation of Gerber-Shiu dis-counted penalty function is obtained. Based on the results, the defective renewal equation of the ruin probability, the moments of the surplus immediately prior to ruin and the deficit at ruin have been deduced. By solving the differential equation, the inequality which the ruin probability satisfied have been obtained when the claim variable random belongs to the expo-nential distribution. Moreover, numerical analysis of the distribution is presented and some examples are given. Finally, we conclude that the impacts of the adjustment policy and the premium policy to the insurance company.