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相对表现视角下的再保险与投资策略

杨鹏1,2,杨志江3   

  1. 1. 西京学院理学院,西安 710123; 2. 西安交通大学数学与统计学院, 西安 710049; 3. 潍坊市工程技师学院电气系, 诸城 262233
  • 出版日期:2021-02-25 发布日期:2021-04-19

杨鹏,杨志江. 相对表现视角下的再保险与投资策略[J]. 系统科学与数学, 2021, 41(2): 517-532.

YANG Peng,YANG Zhijiang. Reinsurance  and Investment Strategies from the Perspective of Relative Performance[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(2): 517-532.

Reinsurance  and Investment Strategies from the Perspective of Relative Performance

YANG Peng 1,2 ,YANG Zhijiang3   

  1. 1. School of Science, Xijing University, Xi’an 710123; 2. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049; 3. Department of Electrical, Weifang Engineering Technician College, Zhucheng 262233
  • Online:2021-02-25 Published:2021-04-19

从相对表现视角, 量化了保险公司与再保险公司在签订再保险合约时的竞争, 进而研究了它引起的时间一致的再保险和投资策略选择问题. 保险公司的盈余过程满足复合泊松风险模型, 考虑投资时假设金融市场由一个无风险资产和$n$个相关的风险资产组成. 保险公司的研究目标是: 寻找最优再保险和投资策略最大化终止财富的均值, 同时最小化终止财富的方差. 该问题是时间不一致的, 文章从博弈的框架对其进行了研究. 应用随机控制理论, 求得了时间一致最优再保险和投资策略以及相应最优值函数的显式解. 进而, 得到了考虑相对表现时, 保险公司对再保险策略的修正方式, 同时得到了保险公司是否在某个具体风险资产上投资的准则. 最后, 通过理论分析和数值实验解释了模型参数对时间一致最优再保险和投资策略的影响, 得到了一些深刻的经济见解.

From the perspective of relative performance, this paper quantifies the competition between an insurance company and a reinsurance company when signing reinsurance contract, and then studies the resulting time-consistent reinsurance and investment strategy selection problem. The insurance company's surplus process is modulated by a compound Poisson process, and the financial market consists of one risk-free asset and $n$ risky assets with dependence. The objective of the insurance company is to choose an optimal reinsurance-investment strategy so as to maximize the expected terminal surplus while minimizing the variance of the terminal surplus. Since this problem is time-inconsistent, we attack it by placing the problem within a game theoretic framework. By applying stochastic control theory, explicit solutions for the optimal time-inconsistent reinsurance-investment strategy and the corresponding optimal value functions are obtained. Furthermore, we obtain the revision method of reinsurance strategy when considering relative performance, meanwhile, obtain the criteria of whether the insurance company invests in a specific risky asset. Finally, through theoretical analysis and numerical experiments, the influence of model parameters on the time-consistent optimal reinsurance-investment strategy is explained, and some meaningful economic insights or implications are provided.

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