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Optimal mean–variance investment and reinsurance problem for an insurer with stochastic volatility

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  • Zhongyang Sun

    (Nankai University)

  • Junyi Guo

    (Nankai University)

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.

Suggested Citation

  • Zhongyang Sun & Junyi Guo, 2018. "Optimal mean–variance investment and reinsurance problem for an insurer with stochastic volatility," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(1), pages 59-79, August.
    • Handle: RePEc:spr:mathme:v:88:y:2018:i:1:d:10.1007_s00186-017-0628-7
    DOI: 10.1007/s00186-017-0628-7
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    References listed on IDEAS

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    3. Yumo Zhang, 2021. "Dynamic Optimal Mean-Variance Investment with Mispricing in the Family of 4/2 Stochastic Volatility Models," Mathematics, MDPI, vol. 9(18), pages 1-25, September.
    4. Yingxu Tian & Zhongyang Sun & Junyi Guo, 2022. "Optimal Mean-Variance Investment-Reinsurance Strategy for a Dependent Risk Model with Ornstein-Uhlenbeck Process," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1169-1191, June.
    5. Yumo Zhang, 2022. "Dynamic optimal mean-variance portfolio selection with stochastic volatility and stochastic interest rate," Annals of Finance, Springer, vol. 18(4), pages 511-544, December.
    6. Wei Wang & Qianyan Li & Quan Li & Song Xu, 2023. "Robust Optimal Investment Strategies with Exchange Rate Risk and Default Risk," Mathematics, MDPI, vol. 11(6), pages 1-17, March.
    7. Zhang, Caibin & Liang, Zhibin, 2022. "Optimal time-consistent reinsurance and investment strategies for a jump–diffusion financial market without cash," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).

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