基于非对称信息的最优再保险合同设计

最优再保险合同设计是保险精算领域的热点问题之一，最优的再保险保单需要从保险人和再保险人的双方利益共同出发来制定。本项目拟研究非对称信息下的最优再保险策略。研究内容包括：首先，在双方非对称信息和异质信念下，借助于扭曲风险测度研究多类保险人与再保险人之间的最优鲍利再保险保单。其次，从风险管理的角度利用经济学上的委托代理模型建立激励相容约束条件，制定多类保险人最优的或次优的利普希茨类型再保险合同，分别讨论成数分保、有限止损、成数分保与简单止损混合保单下的参数确定问题，并推广至双方具有异质信念的框架下。最后，对于上述两个问题背景下导出的分层再保险策略，研究保险人的保单限额及免赔额的最优分配策略，并将相应研究结果推广到随机化的再保险保单情形之下。预期研究成果可为再保险人制定优质保单及保险人有效降低自身风险提供理论支撑与技术支持。

The problem of optimal reinsurance design is one of hot research topics in the area of actuarial science. The optimal reinsurance contract should be designed from the viewpoints of both the reinsurer and the insurer. The current project studies optimal reinsurance strategies under asymmetric information. The study contains: Firstly, with the help of distortion risk measures, we shall design optimal Bowley reinsurance contract between multiple types of insurers and a reinsurer under asymmetric information and heterogeneous beliefs. Secondly, by adopting the well-known principal-agent model arising in economics, the optimal or suboptimal 1-Lipschitz type reinsurance policy will be derived for multiple types of insurers and a reinsurer under some incentive compatible constraints. We shall also determine the parameters in some explicit policies including the quota-share policy, stop-loss contract with an upper limit, and the mixture of the quota-share policy and stop-loss policy. Furthermore, we generalize the above results to the framework where both parties have heterogeneous beliefs on the risk distributions. Thirdly, for the optimal reinsurance contracts with layers derived from the previous two problems, we shall study the optimal allocation problem of deductibles and policy limits from the viewpoint of the insurer, and then extend the promising results to the case of randomized stop-loss policies with layers. The research results of this project are expected to provide theoretical foundation and technical support for the reinsurer to design reinsurance contracts with high quality, and for the insurer to reduce its own retained risk in a better way.