在一个推广后的Poisson风险模型下的破产概率

风险理论作为保险精算数学的一部分 ,主要处理保险事务中的随机风险模型并研究破产概率等问题。经典复合Poisson风险模型是主要的研究对象之一。在此模型下 ,保险公司按照单位时间常数速率收取保单 ,假定每张保单的保费相同。但在实际中 ,不同单位时间所收取的保单数常常不一样 ,是一个随机变量 ,可能服从某一离散分布。根据这一实际情况 ,将经典的复合Poisson风险模型进行了推广 ,将保单收入过程推广为一个参数为α >0的Poisson过程 ,并假定它与理赔过程独立 ,然后运用随机过程和鞅论的方法得出了推广后的Poisson模型的破产概率满足的Lundberg不等式和一般公式。最后得出了当个体索赔服从指数分布时破产概率的具体表达式。

RUIN PROBABILITY IN A GENERALIZED POISSON RISK MODEL

Risk theory, as a part of insurance-or actuarial-mathematics, deals with stochastic models of an insurance business and studies the probability of ruin. The classical compound Poisson risk model is one of principal models. In such a model, the company receives a certain numbers of policies, which every policy has the same premiums,but in fact,the numbers of policy that the company received during the different unit time are different. Based on this fact,the classical compound Poisson risk model to a new risk model are generalized, which the arrival of term policies is a Poisson process. Then the Lundberg inequality and the formula for the ruin probability in this new model through stochastic process and martingale theory are concluded. Finally, the formula for the ruin probability is got in case of exponential claim amounts.