Abstract
This paper considers an optimal investment and reinsurance problem for an insurer under the mean–variance criterion. The stochastic volatility of the stock price is modeled by a Cox-Ingersoll-Ross (CIR) process. By applying a backward stochastic differential equation (BSDE) approach, we obtain a BSDE related to the underlying investment and reinsurance problem. Then solving the BSDE leads to closed-form expressions for both the efficient frontier and the efficient strategy. In the end, numerical examples are presented to analyze the economic behavior of the efficient frontier.
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Acknowledgements
The authors would like to thank Prof. Xianping Guo (Sun Yat-sen University) for his valuable suggestions. The authors also thank the referees for their careful reading of the paper and helpful comments. The project on which this research is based has been carried out with funding provided by the National Natural Science Foundation of China (Grant Nos. 11571189, 11701087) and the China Postdoctoral Science Foundation (Grant No. 2017M612787).
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Sun, Z., Guo, J. Optimal mean–variance investment and reinsurance problem for an insurer with stochastic volatility. Math Meth Oper Res 88, 59–79 (2018). https://doi.org/10.1007/s00186-017-0628-7
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DOI: https://doi.org/10.1007/s00186-017-0628-7
Keywords
- Mean–variance criterion
- CIR process
- Backward stochastic differential equation
- Efficient frontier
- Efficient strategy