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Optimal Reinsurance and Investment Strategies Under Mean-Variance Criteria: Partial and Full Information

ZHU Shihao, SHI Jingtao   

  1. School of Mathematics, Shandong University, Jinan 250100, China
  • Received:2020-09-25 Revised:2021-07-26 Online:2022-08-25 Published:2022-08-02
  • Supported by:
    This paper was supported by National Key R&D Program of China under Grant No. 2018YFB1305400, the National Natural Science Foundations of China under Grant Nos. 11971266, 11831010, 11571205, and Shandong Provincial Natural Science Foundations under Grant Nos. ZR2020ZD24, ZR2019ZD42.

ZHU Shihao, SHI Jingtao. Optimal Reinsurance and Investment Strategies Under Mean-Variance Criteria: Partial and Full Information[J]. Journal of Systems Science and Complexity, 2022, 35(4): 1458-1479.

This paper is concerned with an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance. The driving Brownian motion and the rate in return of the risky asset price dynamic equation cannot be directly observed. And the short-selling of stocks is prohibited. The problem is formulated as a stochastic linear-quadratic control problem where the control variables are constrained. Based on the separation principle and stochastic filtering theory, the partial information problem is solved. Efficient strategies and efficient frontier are presented in closed forms via solutions to two extended stochastic Riccati equations. As a comparison, the efficient strategies and efficient frontier are given by the viscosity solution to the HJB equation in the full information case. Some numerical illustrations are also provided.
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