一类带投资和干扰的双到达过程风险模型

A Kind of Double Arrival Process Risk Model with Investment and Disturbance

研究了一类带投资和干扰的双到达过程风险模型,其中保费收取为时间t的线性函数而两种索赔均为复合Poisson过程,并考虑到投资和随机干扰.利用鞅分析得到了该模型下的破产概率的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,而且得出了当索赔都服从指数分布时生存概率的微分方程.本文所得结果对保险公司和保险监管部门设置预警措施可提供一定的理论依据.

In this paper,we considered a kind of double arrival process risk model with investment and disturbance. In the model,the premium income is a linear function of time t and the two arrivals of the claims follow compound Poisson processes. Moreover,we took investment and random disturbance into account. Using martingale analysis,we obtained the Lundberg inequality and the accurate expression of ruin probability. Using differential calculus and Ito formula,we obtained the integro-differential equation for survival probability. When the claims were exponentially distributed,we derived a differential equation for the survival probability. The results of this paper provide some theoretical guidance and have application values for the insurance companies and insurance regulatory authorities to set up early warning measures.