一类保费和理赔随机的风险模型

A class of risk model with random premium income and random claim sizes

为求得风险事件和理赔事件不等价情况下风险模型的破产概率,基于复合Poisson-Geometric过程和复合Poisson过程,考虑随机利率、两险种、保险公司不确定的收益和单位时间的支出费用,研究了一类保费和理赔随机的风险模型.运用鞅论的方法研究得出破产概率公式及其上界,结合经验数据得出破产概率与利率的关系式.研究结果表明:破产概率随着利率的增大而减小,应加强投保的普遍性,促进保险公司的稳定经营.

In order to obtain the ruin probability of the risk model in which the risk events and the claim events are not equivalent, based on compound Poisson process and compound Poisson-Geometric process, a class of risk model with random premium income and random claim sizes was studied, in which stochastic interest rate,two-type-risk insurance, random disturbance term and expenses per unit time were considered. The ruin probability formula and bound from upper were obtained by martingale approach, and based on empirical data, the relation between ruin probability and interest rate was obtained. The conclusions show that the ruin probability decreases with interest increasing. The insure universality should be strengthened, which improves the operation stability of insurance companies.