【作者】 朱晓霞；

【导师】 韩东；

【作者基本信息】 上海交通大学 ， 概率论与数理统计， 2011， 硕士

【摘要】 再保险是保险人为了分散风险而将全部或部分保险业务转移给另一个保险人的保险。本文综合考虑原保险公司、再保险公司的利益,在期望保费原则下,以两方或多方的联合生存概率最大作为最优准则。对于只有一家再保险公司的情形,假设X为原保险公司所面临的风险, f ( X )为原保险公司分出给再保险公司的部分风险,其中, f ( x )是单调递增的凸函数。本文证明最优的转移损失函数f ( x )在函数族中,其中包括定义在上的形式为:的所有非负函数。对于实务中常见的三种再保险形式:比例再保险、停止损失再保险、变换损失再保险,我们讨论了具体参数的最优解并给出数值例子。在实际中,一家保险公司可以同时向另几家保险公司转移风险。本文建立联合生存概率准则下的多重最优再保险模型。给出多重比例再保险、多重停止损失—比例混合再保险的最优策略。研究发现,随着参与的再保险公司数目的增多,联合生存概率增大,也就是说,为了提高生存概率,保证经营的稳定性,原保险公司应该向更多的再保险公司分保风险。更多还原

【Abstract】 Reinsurance is an insurance policy which transfers all or part of insurance business in order to scatter the risk to another insurer. In this paper , we consider both the insurer’s benefits and reinsurer’s benefits by using their joint survival probability as the criteria for determining the optimal reinsurance.Let X be the loss initially assumed by an insurer. In a reinsurance design, the insurer cedes parts of its loss, say f ( X ),where f ( x ) is increasing convex and known as a ceded loss function . In this paper , we prove that the function with the form of , ,the optimal ceded loss function under joint survival probability criterion. To practice common reinsurance form , we derive optimal quota- share reinsurance strategy , optimal stop-loss reinsurance strategy and optimal change-loss reinsurance strategy under the expectation premium principle. A number of concrete numerical examples are also shown.In practice , an insurance company can simultaneously transfer the initial loss to two or more reinsurance companies . Therefore , this paper formulate and study optimal reinsurance model with m reinsurance companies under the joint survival probability ctiteria . The results indicate that the joint survival probability increases if more reinsurance companies take risk. In other words, in order to improve survival probability and guarantee the stability of the business , the original insurance company should cedes parts of its loss to more reinsurance companies.更多还原