一类带干扰的Cox风险模型

A Cox risk model perturbed by diffusion

将[1][2]的风险模型推广到带干扰的一种新的模型,使得该模型更能符合实际要求。模型中保单到达过程和理赔到达过程都是Cox过程,且保费的收入过程是一个独立同分布的随机序列。应用鞅论的方法,得出破产概率的一个不等式。并给出了在没有干扰且保单到达过程和理赔到达过程具有相同累计强度过程时破产概率的明确表达式。

In this paper, we generalize the classical risk model that perturbed by diffusion, that is, the arrival of policies and the claims are Cox process, and the premium income process is an i. i. d. random sequence. By using the method of Martingale, we get the inequality for the ultimately ruin probability. And an explicit expression is given when there is no diffusion and the arrival of the policies and the occurrence of the claims has the same intensity process.