保险公司之间基于Thinning相依风险模型的投资与再保险博弈研究

近几年来，保险公司的最优投资与再保险问题是保险精算领域研究的热点话题。相关研究通常是基于独立风险模型以及站在单个保险公司的角度。然而随着金融全球化进程的加快，保险公司之间不仅保险业务的相互依赖关系变得越来越强，而且它们的合作与竞争也日趋频繁。因此，以往在独立风险模型及单方角度下的研究存在一些局限性。本项目采用Thinning风险模型刻画相互依赖的保险业务，利用随机分析理论、随机控制理论和随机微分博弈方法，致力于探讨保险公司与保险公司、保险公司与再保险公司以及它们在信息不对称情形下的投资与再保险博弈问题。主要创新有两个方面：一是在Thinning相依风险模型下探讨多个保险公司的博弈决策问题；二是在Thinning相依风险模型下将信息不对称现象纳入风险模型进行研究。该项目的预期成果有望为保险公司的科学决策提供理论依据，促进数学与统计学科和保险之间的交叉融合，丰富风险管理与保险精算理论。

In recent years, the optimization of investment and reinsurance for insurers has been a hot topic in actuarial science. The standard discussion is usually based on independent risk models and only from the perspective of an insurer. However, with the speed of the global finance, the dependence among the insurance businesses becomes increasingly stronger, and the cooperation and competition among firms are becoming increasingly frequent as well. Therefore, the previous researches on independent risk models and unilateral perspective have some limitations. Using the thinning risk model to describe the dependent insurance businesses and by the stochastic analysis and stochastic control theory and stochastic differential game method, this project focuses on the investment and reinsurance games between insurer and insurer, insurer and reinsurer, as well as they are in the situation of the information asymmetry. We have the innovations on the following points: Firstly, this project discusses some game decision problems for multiple insurance companies under the thinning dependent risk model; Secondly, the phenomenon of the information asymmetry is considered into the researches based on the thinning dependent risk model. The research results of this project may provide some scientific references for insurance companies decisions, promote the intersection and merging of insurance science with mathematics and statistics, and further enrich the results of risk management and actuarial theory.