连续时间模型下的动态随机合作再保险策略

Dynamic stochastic cooperative reinsurance strategy in a continuous time model

如何通过选择再保险策略以最大化保险公司的终端期望效用是保险精算领域中的一个热门研究话题.这个问题在单期离散模型下已经有了很好的研究结果.本文首次考虑了连续时间模型下的最优动态合作再保险问题.基于互惠的再保险概念和指数效用函数,本文引入了博弈论中的Pareto最优概念,给出了含有Pareto最优合作再保险策略的核的界定方法并证明此核是非空的.通过实例,验证了合作再保险博弈的核的非空性,并且得出了在两家保险公司的情形下(保险公司和再保险公司),Pareto最优合作再保险策略是比例再保险策略.

The problem of the expected utility maximization in a reinsurance market for a single period model is well understood under a general setting. This paper studies the problem in a continuous time model. For reciprocal type of reinsurance strategies and exponential utility functions, with the concept of the Pareto optimality in game theory, we obtain the characterization of the core of cooperative reinsurance games and show that the core, which contains all of the Pareto optimal cooperative reinsurance strategies, is non-empty. Examples are provided to illustrate that the core is non-empty under the given situations and the Pareto optimal cooperative reinsurance strategy is shown to be a proportional reinsurance strategy when there are only two insurance companies considered.