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

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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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 (2021). https://doi.org/10.1007/s11009-021-09902-5

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Keywords

  • Optimal investment-reinsurance strategy
  • Common shock
  • Mean-reverting processes
  • Backward stochastic differential equation
  • Efficient frontier

Mathematics Subject Classification (2000)

  • 62P05
  • 93E20