一类带干扰的复合Poisson-Geometric过程风险模型

A Kind of Compound Poisson-Geometric Process Risk Model with Disturbance

研究了一类带干扰的双到达过程风险模型,其中保费收取为时间t的线性函数而两险种的索赔均为复合Poisson-Geometric过程.利用鞅分析得到了该模型的破产概率的Lundberg不等式及其精确表达式;利用微分和It公式得到了生存概率的积分微分方程.该模型所得到的结果可对保险公司和保险监管部门设置预警措施提供一定的理论指导,具有实际应用价值.

In this paper, we considered a kind of double arrival process risk model with disturbance. In the model, the premium income is a linear function of time t and the two arrivals of the claims follow compound Poisson-Geometric processes. Using martingale analysis, we obtained the Lundberg inequality and the accurate expression of ruin probability ; using differential calculus and It＇s formula, we obtained the integro-differential equation for survival probability. The results of the model in this paper can provide some theoretical guidance and have practical application values for the insurance companies and insurance regulatory authorities when they set up early warning measures.