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Optimal Mean-Variance Investment-Reinsurance Strategy for a Dependent Risk Model with Ornstein-Uhlenbeck Process

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Abstract

In this paper, we investigate the optimal investment-reinsurance strategy for an insurer with two dependent classes of insurance business, where the claim number processes are correlated through a common shock. It is assumed that the insurer can invest her wealth into one risk-free asset and multiple risky assets, and meanwhile, the instantaneous rates of investment return are stochastic and follow mean-reverting processes. Based on the theory of linear-quadratic control, we adopt a backward stochastic differential equation (BSDE) approach to solve the mean-variance optimization problem. Explicit expressions for both the efficient strategy and efficient frontier are derived. Finally, numerical examples are presented to illustrate our results.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grant Nos. 11901344, 11931018, 12101602), the Fundamental Research Funds for the Central Universities (Grant No. 3122019139, 3122019156), the Shandong Provincial Natural Science Foundation, China (Grant No. ZR2019QA013), and Scientific Research Foundation for Introduced Scholars of Civil Aviation University of China (Grant No. 2020KYQD104).

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Authors and Affiliations

  1. College of Science, Civil Aviation University of China, Tianjin, 300300, P.R. China

    Yingxu Tian

  2. School of Statistics, Qufu Normal University, Qufu, 273165, Shandong, P.R. China

    Zhongyang Sun

  3. School of Mathematical Sciences, Nankai University, Tianjin, 300071, P.R. China

    Junyi Guo

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  1. Yingxu Tian
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  2. Zhongyang Sun
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  3. Junyi Guo
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Correspondence to Zhongyang Sun.

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Tian, Y., Sun, Z. & Guo, J. Optimal Mean-Variance Investment-Reinsurance Strategy for a Dependent Risk Model with Ornstein-Uhlenbeck Process. Methodol Comput Appl Probab 24, 1169–1191 (2022). https://doi.org/10.1007/s11009-021-09902-5

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  • DOI: https://doi.org/10.1007/s11009-021-09902-5

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