一类带干扰的双险种风险模型破产概率的鞅分析

Martingale analysis of insurance risk model of bankruptcy with perturbed random collection of insurance

在经典带干扰Poisson模型的基础上,假设理赔额到达过程和保单的到达过程为泊松过程,保单的保费和各险种的理赔额均为随机序列,并考虑到保险公司的投资利率的通货膨胀率,讨论了一类带干扰的保费随机收取的双险种风险模型.利用鞅分析得到了该模型下破产概率的Lundberg不等式及其精确表达式.

In this paper, based on the classical Poisson model with interference, assumed that the arrival process of the amount of claim and the insurance policy as the Poisson process, both the policy premiums and the insurance settlement of claims were random sequences; Took the inflation rate of the insurance company＇ s investment interest rates into account, a kind of perturbed random premium dual - risk model was discussed. And used martingale analysis to derive the Lundberg inequality and its accurate expression of ruin probability under this model.