• 论文 •

### 相对表现视角下的再保险与投资策略

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

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

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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