Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2024, Vol. 41 ›› Issue (1): 1-16.doi: 10.3969/j.issn.1005-3085.2024.01.001

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Robust Optimal Reinsurance and Investment Strategy with Delay under Mean-variance Premium Principle

HU Jingming1,  LIU Wei1,  YAN Fang1,  HU Yijun2   

  1. 1. College of Mathematics and System Science, Xinjiang University, Urumqi 830046;
    2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072
  • Received:2021-11-01 Accepted:2022-07-09 Online:2024-02-15 Published:2024-04-15
  • Supported by:
    The National Natural Science Foundation of China (11961064; 71102118).

Abstract:

The problem of robust optimal reinsurance and investment strategies for insurance companies with time delay are investigated. By purchasing proportional reinsurance, insurance companies can transfer a portion of their claim risks and pay reinsurance premiums based on the general mean-variance premium principle. At the same time, insurance companies invest their assets in a financial market consisting of a risk-free asset and a risky asset. Assume that the instantaneous expected return rate of the risky asset follows a mean-reverting Ornstein-Uhlenbeck (O-U) process. To maximize the exponential utility expectation of the insurance company's terminal wealth, dynamic programming principles are applied. By solving the Hamilton-Jacobi-Bellman (HJB) equation, the optimal reinsurance-investment strategy and the corresponding explicit expression of the value function are obtained. Furthermore, numerical analysis shows the impact of the main parameters on the optimal strategy. The results reveal that reinsurance strategy is mainly affected by the parameters of the insurance market and risk-free asset models, rather than the risky asset model or expected return rate. Time delay and robustness factors have a significant impact on the optimal reinsurance-investment strategy. Considering time delay improves the stability of the company's wealth while incorporating model uncertainty reduces the risk from inaccurate probability measures.

Key words: stochastic optimal control, robust, delay, reinsurance-investment strategy, mean-variance premium principle

CLC Number: