完全离散复合二项风险模型破产概率的一个新求法

A NEW METHOD OF CALCULATING THE RUIN PROBABILITY IN FULLY DISCRETE COMPOUND BINOMIAL RISK MODEL

本文主要利用过程的马尔可夫性对完全离散复合二项风险模型进行研究,首先得到了赔付间断时间序列和赔付时刻赢余的有限维联合密度,然后根据这一结论,得到了新的破产概率公式以及有限时间内的生存概率公式,并在当初始资本u=0,c=1,赔付随机变量服从赌徒分布即P(Yi=2)=1,i=1,2,3,…的情况下,得到了有限时间内的生存概率.

In this paper we considered the fully discrete compound binomial risk model. At first, we got the joint probability distribution of the gaps of the losses and the capitals at just happening claim, then we got the formulas of the ruin probability and survival probability of an insurance company having initial capital u. At last, we discussed the classical gambler＇s ruin model, when u=0 and which in this case at each time unit an increase in the reserve of 1 occurs with probability q and a decrease of 1 occurs with probability p.