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Optimal investment and reinsurance strategies for insurers with generalized mean–variance premium principle and no-short selling

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  • Zhang, Xin
  • Meng, Hui
  • Zeng, Yan

Abstract

This paper analyzes the optimal investment and reinsurance strategies for insurers with a generalized mean–variance premium principle. The surplus process of the insurer is described by the diffusion model which is an approximation of the classical Cramér–Lundberg model. The insurer can purchase reinsurance and invest her surplus in a financial market consisting of a risk-free asset and multiple risky assets. The insurer is not allowed to short sell the risky assets. Two optimization problems, maximizing the expected utility function of terminal wealth and minimizing the probability of ruin, are considered. We first derive the form of optimal reinsurance for the two optimization problems. Then, by using the stochastic dynamic programming, we obtain the closed-form expressions of optimal investment and reinsurance strategies and optimal value functions for the two optimization problems. We find that our results are more general than some ones in the existing literature.

Suggested Citation

  • Zhang, Xin & Meng, Hui & Zeng, Yan, 2016. "Optimal investment and reinsurance strategies for insurers with generalized mean–variance premium principle and no-short selling," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 125-132.
    • Handle: RePEc:eee:insuma:v:67:y:2016:i:c:p:125-132
    DOI: 10.1016/j.insmatheco.2016.01.001
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    References listed on IDEAS

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    Cited by:

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    2. Chen, Lv & Shen, Yang, 2019. "Stochastic Stackelberg differential reinsurance games under time-inconsistent mean–variance framework," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 120-137.
    3. Zhang, Nan & Jin, Zhuo & Qian, Linyi & Fan, Kun, 2019. "Stochastic differential reinsurance games with capital injections," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 7-18.
    4. Chen, Lv & Qian, Linyi & Shen, Yang & Wang, Wei, 2016. "Constrained investment–reinsurance optimization with regime switching under variance premium principle," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 253-267.
    5. Sun, Jingyun & Yao, Haixiang & Kang, Zhilin, 2019. "Robust optimal investment–reinsurance strategies for an insurer with multiple dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 157-170.
    6. Yan, Tingjin & Wong, Hoi Ying, 2020. "Open-loop equilibrium reinsurance-investment strategy under mean–variance criterion with stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 105-119.
    7. Meng, Hui & Wei, Li & Zhou, Ming, 2023. "Multiple per-claim reinsurance based on maximizing the Lundberg exponent," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 33-47.
    8. Liu, Bing & Meng, Hui & Zhou, Ming, 2021. "Optimal investment and reinsurance policies for an insurer with ambiguity aversion," The North American Journal of Economics and Finance, Elsevier, vol. 55(C).
    9. Liang, Xiaoqing & Liang, Zhibin & Young, Virginia R., 2020. "Optimal reinsurance under the mean–variance premium principle to minimize the probability of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 128-146.
    10. Koch-Medina, Pablo & Moreno-Bromberg, Santiago & Ravanelli, Claudia & Šikić, Mario, 2021. "Revisiting optimal investment strategies of value-maximizing insurance firms," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 131-151.
    11. Wang, Ning & Zhang, Nan & Jin, Zhuo & Qian, Linyi, 2021. "Stochastic differential investment and reinsurance games with nonlinear risk processes and VaR constraints," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 168-184.
    12. Hiroaki Hata & Shuenn-Jyi Sheu & Li-Hsien Sun, 2019. "Expected exponential utility maximization of insurers with a general diffusion factor model : The complete market case," Papers 1903.08957, arXiv.org.
    13. Chen, Shumin & Liu, Yanchu & Weng, Chengguo, 2019. "Dynamic risk-sharing game and reinsurance contract design," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 216-231.
    14. Wang, Hao & Wang, Rongming & Wei, Jiaqin, 2019. "Time-consistent investment-proportional reinsurance strategy with random coefficients for mean–variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 104-114.
    15. Jiaqi Zhu & Shenghong Li, 2020. "Time-Consistent Investment and Reinsurance Strategies for Mean-Variance Insurers under Stochastic Interest Rate and Stochastic Volatility," Mathematics, MDPI, vol. 8(12), pages 1-22, December.
    16. Wang, Ning & Zhang, Nan & Jin, Zhuo & Qian, Linyi, 2019. "Robust non-zero-sum investment and reinsurance game with default risk," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 115-132.
    17. Meng, Hui & Liao, Pu & Siu, Tak Kuen, 2019. "Continuous-time optimal reinsurance strategy with nontrivial curved structures," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    18. Fudong Wang & Zhibin Liang, 2022. "Optimal Per-Loss Reinsurance for a Risk Model with a Thinning-Dependence Structure," Mathematics, MDPI, vol. 10(23), pages 1-23, December.

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    More about this item

    Keywords

    Investment and reinsurance; Generalized mean–variance premium principle; Expected utility; Ruin probability; Stochastic control;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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