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Equilibria and efficiency in a reinsurance market

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  • Zhu, Michael B.
  • Ghossoub, Mario
  • Boonen, Tim J.

Abstract

We study equilibria in a reinsurance market with multiple reinsurers that are endowed with heterogeneous beliefs, where preferences are given by distortion risk measures, and pricing is done via Choquet integrals. We construct a model in the form of a sequential economic game, where the reinsurers have the first-mover advantage over the insurer, as in the Stackelberg setting. However, unlike the Stackelberg setting, which assumes a single monopolistic reinsurer on the supply side, our model accounts for strategic price competition between reinsurers. We argue that the notion of a Subgame Perfect Nash Equilibrium (SPNE) is the appropriate solution concept for analyzing equilibria in the reinsurance market, and we characterize SPNEs using a set of sufficient conditions. We then examine efficiency properties of the contracts induced by an SPNE, and show that these contracts result in Pareto-efficient allocations. Additionally, we show that under mild conditions, the insurer realizes a strict welfare gain, which addresses the concerns of Boonen and Ghossoub (2022) with the Stackelberg model and thereby ultimately reflects the benefit to the insurer of competition on the supply side. We illustrate this point with a numerical example.

Suggested Citation

  • Zhu, Michael B. & Ghossoub, Mario & Boonen, Tim J., 2023. "Equilibria and efficiency in a reinsurance market," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 24-49.
    • Handle: RePEc:eee:insuma:v:113:y:2023:i:c:p:24-49
    DOI: 10.1016/j.insmatheco.2023.07.004
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    References listed on IDEAS

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    14. Tim J. Boonen & Fangda Liu & Ruodu Wang, 2021. "Competitive equilibria in a comonotone market," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(4), pages 1217-1255, November.
    15. Cheung, Ka Chun & Yam, Sheung Chi Phillip & Zhang, Yiying, 2019. "Risk-adjusted Bowley reinsurance under distorted probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 64-72.
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    Cited by:

    1. Zongxia Liang & Xiaodong Luo, 2024. "Stackelberg reinsurance and premium decisions with MV criterion and irreversibility," Papers 2402.11580, arXiv.org.
    2. Mario Ghossoub & Michael B. Zhu & Wing Fung Chong, 2024. "Pareto-Optimal Peer-to-Peer Risk Sharing with Robust Distortion Risk Measures," Papers 2409.05103, arXiv.org.
    3. Xuelian Li & Shiu-Chieh Chiu & Jyh-Horng Lin & Yuxin Xie, 2024. "Assessing insurer guarantee cover and risk retention toward SDG 3: a structure-break down-and-out call valuation," Palgrave Communications, Palgrave Macmillan, vol. 11(1), pages 1-10, December.
    4. Ghossoub, Mario & Zhu, Michael B., 2024. "Stackelberg equilibria with multiple policyholders," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 189-201.

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    More about this item

    Keywords

    Optimal reinsurance; Bowley optima; Stackelberg equilibria; Subgame perfect Nash equilibria; Pareto efficiency; Choquet pricing; Heterogeneous beliefs;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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