基于凸风险测度与切换控制的保险公司再保险与投资策略研究

According to the current demand for better fund utilization and the request for further risk-based regulation in the insurance industry in our country, this research project, standing at the viewpoint of an insurance company, maily focuses on the following four aspects: (1) Risk control for an insurance company with convex risk measure; (2) Risk management for an insurance company with dynamic risk constraint; (3) Optimal reinsurance and dividend strategy for an insurance company with switching control; (4) Optimal investment-reinsurance strategy for an insurance company in the presence of real investment. We will first model the above problems. Then, by applying the methodology of continuous-time stochastic control, we aim at finding the value functions and the optimal strategies explicitly or numerically. Finally, we will perform some sensitivity analysises to illustrate the results and present their economic implications. The innovation of this research project can be listed as follows: First, it introduces convex risk measure and dynamic risk constraint in risk control for an insurance company. Second, it considers the possibility of real investment, which is an important investment instrument in the insurance industry, whereas, is seldomly considered in previous researches. The third is its application of switching control model in an insurance company's decisionmaking. The contents of this research project belong to the most polular issues in actuarial research and are closely related to current real-life situation. Our results can also provide some economic insights and rational suggestions for both managers and regulators of insurance industry. Therefore this research project has both theoretical and practical significance.

本项目拟根据我国保险行业关于加强资金运用的实际需要，结合当前加强风险监管的实际背景，从保险公司的角度出发，以风险控制为目标，运用随机控制相关理论与方法，研究以下四个方面的问题：(1) 基于凸风险测度的保险公司风险控制问题，(2) 基于动态风险约束的保险公司风险管理问题，(3) 含切换控制的保险公司再保险与分红策略，(4) 含不动产投资项目的保险公司投资与再保险策略。本项目拟建立以上各问题的数学模型，应用随机控制方法求解出最优值函数及最优策略的显式表达式或数值解，对结果进行敏感性分析并予以经济解释。项目的创新之处在于：引入凸风险测度及动态风险约束以控制保险公司风险水平；考虑了不动产投资；将切换控制模型应用于保险公司最优策略研究。本项目紧密联系实际，其研究内容属于当前保险精算领域的研究热点与前沿问题，研究结果可为保险公司及监管部门的运作提供合理的意见及决策依据，因而具有重大理论与现实意义。

本项目考虑保险公司最优投资、再保险、分红与融资决策问题。我们用经典的Cramer-Lundberg风险模型和扩散风险模型描述保险公司流动资金变化，并假定保险公司管理者可将流动资金投资于金融市场，目标是最大化期末财富的效用或保险公司累积分红与融资现值之差。首先，我们考虑分红过程存在比例与固定交易费用、风险约束、管理者时间不一致性偏好等因素对保险公司分红决策的影响。其次，我们考虑保险公司投资过程存在状态相依效用、定价误差和模型不确定性对保险公司投资与再保险决策的影响。本课题的创新和贡献主要有：第一，首次在保险公司分红决策中考虑时间不一致性偏好的影响，拓展了已有的保险精算理论；第二，系统分析了交易费用对保险公司融资与分红决策的影响。第三，定义分红决策中的Nash完美均衡策略，并提出构造这一策略的方法，完善了已有的奇异控制、脉冲控制理论。