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Time-consistent proportional reinsurance and investment strategies under ambiguous environment

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  • Guan, Guohui
  • Liang, Zongxia
  • Feng, Jian

Abstract

In this paper, we study the equilibrium proportional reinsurance and investment strategies for an insurer in an environment with parameter uncertainties. The insurer can buy proportional reinsurance business to hedge its insurance risks. However, the insurer is ambiguous about the insurance claims and risky assets. Specifically, the insurance claim is exponentially distributed and the rate parameter is uncertain. Besides, the return of a stock is uncertain. The insurer holds ambiguous beliefs over these states. The goal of the insurer is to maximize the smooth ambiguity utility proposed in Klibanoff et al. (2005). The equilibrium control is introduced to derive the time-consistent solution. In the end, a sensitivity analysis is presented to show the economic behaviors of the insurer under the smooth ambiguity. Results reveal that the uncertain beliefs play an important role in the equilibrium reinsurance and investment strategies. When the insurer is more risk averse towards ambiguity, the insurer will invest less in the ambiguous asset and more in the non-ambiguous asset.

Suggested Citation

  • Guan, Guohui & Liang, Zongxia & Feng, Jian, 2018. "Time-consistent proportional reinsurance and investment strategies under ambiguous environment," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 122-133.
    • Handle: RePEc:eee:insuma:v:83:y:2018:i:c:p:122-133
    DOI: 10.1016/j.insmatheco.2018.09.007
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    References listed on IDEAS

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    Cited by:

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    2. 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).
    3. Guan, Guohui & Hu, Xiang, 2022. "Equilibrium mean–variance reinsurance and investment strategies for a general insurance company under smooth ambiguity," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
    4. Guan, Guohui & Hu, Jiaqi & Liang, Zongxia, 2022. "Robust equilibrium strategies in a defined benefit pension plan game," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 193-217.
    5. Haiying Zhou & Huainian Zhu, 2024. "Optimal Reinsurance and Derivative-Based Investment Decisions for Insurers with Mean-Variance Preference," Mathematics, MDPI, vol. 12(13), pages 1-20, June.
    6. Guohui Guan & Jiaqi Hu & Zongxia Liang, 2021. "Robust equilibrium strategies in a defined benefit pension plan game," Papers 2103.09121, arXiv.org.

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    More about this item

    Keywords

    Smooth ambiguity control; Proportional reinsurance; Optimal investment; Time-consistent strategy; Equilibrium control law;
    All these keywords.

    JEL classification:

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

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