退保因素下带有随机保费和分红的风险模型

RESEARCH ON THE MODEL OF RANDOMIZED DIVIDEND AND STOCHASTIC PREMIUM

在经典风险模型基础上,考虑到退保事件的发生,讨论含退保因素下保费到达过程、理赔过程、支付红利过程及退保过程均为二项过程。运用鞅方法讨论了该模型盈余过程的性质,给出最终破产概率的表达式和Lundberg上界,并得到在保费额、理赔额、退保额、支付红利额均服从指数分布条件下的破产概率的具体表达式。

According to the actual situation, a practical risk model with a refunding process is introduced. The arrival of the term policies, the occurrences of claim, refunding and dividend are compound binominal processes. We study the nature of this model by applying the martingale approach and get the Lundberg inequality and the formula of the ruin probability. We also give an explicit expression for the ruin probability with that the premium income, the claims, the occurrence of the refunding and the dividend, which are obey exponential distribution.