两类相依保险业务下基于竞争的最优再保险策略

Optimal Reinsurance Strategy Based on Competition Under Two Kinds of Dependent Insurance Business

在再保险合同制定中,保险公司与再保险公司之间是竞争的.利用相对业绩,本文量化了这种竞争.进而假设保险公司从事两类相依保险业务,在竞争下,得到了保险公司的相对财富过程.保险公司的目标是,寻找最优时间一致的再保险策略最大化终端财富的均值同时最小化其方差.通过使用随机分析和随机控制理论,求得了最优时间一致的再保险策略和值函数的显式解,并从理论方面解释了最优解的保险和经济意义.最终,通过数值实验分析了模型参数对最优时间一致再保险策略的影响,比较了两类特殊情形与一般情形下最优再保险策略之间的关系.通过本文的研究得到了一些新的发现,研究结果可以更合理地指导保险公司的再保险决策.

In the formulation of reinsurance contract,the relationship between an insurance company and a reinsurance company is competitive.By using the relative performance,this paper quantifies this kind of competition.Then,we suppose that the insurance company is engaged in two kinds of dependent insurance business,and derive the relative wealth process of the insurance company under the competition.The aim of the insurance company is to find an optimal time-consistent reinsurance strategy so as to maximize the expected terminal wealth and minimize the variance of the terminal wealth.By using stochastic calculus and stochastic control theory,the explicit solutions for the optimal time-consistent reinsurance strategy and the optimal value function are obtained,and the economic significance of the optimal strategy is discussed theoretically.Finally,the influence of model parameters on the optimal time-consistent reinsurance strategy is analyzed through numerical experiments,and the relationship between the optimal reinsurance strategy in two special cases and a general case is compared.Through the research of this paper,some new findings are obtained,which can guide the reinsurance decision of insurance companies more reasonably.