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Robust non-zero-sum stochastic differential reinsurance game

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  • Pun, Chi Seng
  • Wong, Hoi Ying

Abstract

This paper considers the non-zero-sum stochastic differential game problem between two ambiguity-averse insurers (AAIs) who encounter model uncertainty and seek the optimal reinsurance decision under relative performance concerns. Each AAI manages her own risks by purchasing reinsurance with the objective of maximizing the expected utility of her relative terminal surplus with respect to that of her counterparty. The two AAIs’ decisions influence each other through the insurers’ relative performance concerns and the correlation between their surplus processes. We establish a general framework of Nash equilibrium for the associated non-zero-sum game with model uncertainty. For the representative case of exponential utilities, we solve the equilibrium strategies explicitly. Numerical studies are conducted to draw economic interpretations.

Suggested Citation

  • Pun, Chi Seng & Wong, Hoi Ying, 2016. "Robust non-zero-sum stochastic differential reinsurance game," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 169-177.
  • Handle: RePEc:eee:insuma:v:68:y:2016:i:c:p:169-177
    DOI: 10.1016/j.insmatheco.2016.02.007
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    References listed on IDEAS

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    Cited by:

    1. Qian Lei & Chi Seng Pun, 2021. "Nonlocality, Nonlinearity, and Time Inconsistency in Stochastic Differential Games," Papers 2112.14409, arXiv.org, revised Sep 2023.
    2. 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.
    3. Yanfei Bai & Zhongbao Zhou & Helu Xiao & Rui Gao & Feimin Zhong, 2019. "A hybrid stochastic differential reinsurance and investment game with bounded memory," Papers 1910.09834, arXiv.org.
    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. Asmussen, Søren & Christensen, Bent Jesper & Thøgersen, Julie, 2019. "Nash equilibrium premium strategies for push–pull competition in a frictional non-life insurance market," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 92-100.
    6. 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.
    7. Yanfei Bai & Zhongbao Zhou & Rui Gao & Helu Xiao, 2020. "Nash Equilibrium Investment-Reinsurance Strategies for an Insurer and a Reinsurer with Intertemporal Restrictions and Common Interests," Mathematics, MDPI, vol. 8(1), pages 1-26, January.
    8. Yan, Ming & Peng, Fanyi & Zhang, Shuhua, 2017. "A reinsurance and investment game between two insurance companies with the different opinions about some extra information," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 58-70.
    9. Zhu, Huainian & Cao, Ming & Zhang, Chengke, 2019. "Time-consistent investment and reinsurance strategies for mean-variance insurers with relative performance concerns under the Heston model," Finance Research Letters, Elsevier, vol. 30(C), pages 280-291.
    10. Guohui Guan & Jiaqi Hu & Zongxia Liang, 2021. "Robust equilibrium strategies in a defined benefit pension plan game," Papers 2103.09121, arXiv.org.
    11. Søren Asmussen & Bent Jesper Christensen & Julie Thøgersen, 2019. "Stackelberg Equilibrium Premium Strategies for Push-Pull Competition in a Non-Life Insurance Market with Product Differentiation," Risks, MDPI, vol. 7(2), pages 1-23, May.

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