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Optimal reinsurance-investment game for two insurers with SAHARA utilities under correlated markets

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  • Chen, Dengsheng
  • Lu, Zhengyang
  • He, Yong

Abstract

In this paper, we study the optimal reinsurance-investment game between two insurers with the same insurance business but different wealth and risk preferences. Assume that the insurers who have the symmetric asymptotic hyperbolic absolute risk aversion (SAHARA) utilities and the price of risky asset obeys the constant elasticity of variance (CEV) model. It is impossible to obtain closed-form solution of the optimal reinsurance-investment strategy due to the non-homothetic property and the complicity of SAHARA utilities. According to establish a strong duality relationship of the value function, we successfully propose an efficient dual control Monte Carlo method for computing the Nash equilibrium strategies. Finally, numerical analysis is given to illustrate the impact of model parameters to Nash equilibrium strategies.

Suggested Citation

  • Chen, Dengsheng & Lu, Zhengyang & He, Yong, 2023. "Optimal reinsurance-investment game for two insurers with SAHARA utilities under correlated markets," The North American Journal of Economics and Finance, Elsevier, vol. 68(C).
    • Handle: RePEc:eee:ecofin:v:68:y:2023:i:c:s1062940823000724
    DOI: 10.1016/j.najef.2023.101949
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    References listed on IDEAS

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    1. Sid Browne, 1995. "Optimal Investment Policies for a Firm With a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Mathematics of Operations Research, INFORMS, vol. 20(4), pages 937-958, November.
    2. Browne, S., 1995. "Optimal Investment Policies for a Firm with a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Papers 95-08, Columbia - Graduate School of Business.
    3. Chen, An & Vellekoop, Michel, 2017. "Optimal investment and consumption when allowing terminal debt," European Journal of Operational Research, Elsevier, vol. 258(1), pages 385-397.
    4. Aihua Zhang & Christian-Oliver Ewald, 2010. "Optimal investment for a pension fund under inflation risk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(2), pages 353-369, April.
    5. Bai, Yanfei & Zhou, Zhongbao & Xiao, Helu & Gao, Rui & Zhong, Feimin, 2022. "A hybrid stochastic differential reinsurance and investment game with bounded memory," European Journal of Operational Research, Elsevier, vol. 296(2), pages 717-737.
    6. Ma, Jingtang & Li, Wenyuan & Zheng, Harry, 2020. "Dual control Monte-Carlo method for tight bounds of value function under Heston stochastic volatility model," European Journal of Operational Research, Elsevier, vol. 280(2), pages 428-440.
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    Cited by:

    1. Peng, Xingchun & Wang, Yushuang, 2024. "A non-zero-sum investment and reinsurance game between two mean–variance insurers with dynamic CVaR constraints," The North American Journal of Economics and Finance, Elsevier, vol. 70(C).
    2. Yang Liu & Zhenyu Shen, 2024. "PSAHARA Utility Family: Modeling Non-monotone Risk Aversion and Convex Compensation in Incomplete Markets," Papers 2406.00435, arXiv.org, revised Nov 2024.

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    More about this item

    Keywords

    Reinsurance-investment game; SAHARA utility; Nash equilibrium; Correlated markets; Dual methods; Monte Carlo simulation;
    All these keywords.

    JEL classification:

    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • 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

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