索赔为稀疏过程的双复合 Poisson风险模型

研究了一类风险过程,其中保费收入为复合Poisson过程,而描述索赔发生的计数过程为保单到达过程的p-稀疏过程.给出了生存概率满足的积分方程及其在指数分布下的具体表达式,得到了破产概率满足的Lundberg不等式、最终破产概率及有限时间内破产概率的一个上界和生存概率的积分-微分方程,且通过数值例子,分析了初始准备金、保费收入、索赔支付及保单的平均索赔比例对保险公司破产概率的影响.

Two Compound Poisson Risk Model about that Claims is Thinning Process

A risk model was studied,in which the premium income follows compound Poisson processes and the arrival of the claims is a p-thinning processes of the arrival process.The integral equation of the survival probability and the explicit formula of the survival probability in case of exponential were obtnined.And the Lundberg inequality of the ruin probability,ultimate ruin probability,a upper bound for the ruin probability and the integral-differential equation of the survival probability in finite time were obtained.Meanwhile,the effects of the initial capital,claim amounts,policy amounts and proportions of the claim on the ruin probability of insurance company were analyzed by a numerical example.