一类风险模型的破产概率

Ruin Probability for a Class of Risk Model

考虑了一类多险种多索赔情形的风险模型.首先,证明了调节系数的存在唯一性,进而利用鞅的相关不等式及性质,得到了破产概率的Lundberg不等式及一般表达式;然后,通过模型转换,考虑充分小时段内的索赔情况,利用全概率公式得到了生存概率满足的积分-微分方程;最后,考虑两险种且索赔额服从指数分布这一特定情况,结合前面得到的积分-微分方程和经典风险理论的结果,给出了该特定情况下破产概率的显式表达式.

In this paper, we consider a risk model with multiple insurance business, and each of which involves multiple claim cases. First, the existence and uniqueness of the adjustment coefficient are proved, and Lundberg inequality and the gen-eralized expression of ruin probability are obtained by using inequality and properties of martingale; Second, claim cases in small enough interval are analyzed？ then the integro-differential equation for survival probability is obtained by transforming model and using total probability formula; Finally, based on the preceding integro-differential equation and the results in classi-cal risk theory, the explicit expression of ruin probability is given under a certain conditions that the risk model has two insur-ance business and claims follow the exponential distributions.