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The Nash Bargaining Solution vs. Equilibrium in a Reinsurance Syndicate

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  • Aase, Knut K.

    (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration)

Abstract

We compare the Nash bargaining solution in a reinsurance syndicate to the competitive equilibrium allocation, focusing on uncertainty and risk aversion. Restricting attention to proportional reinsurance treaties, we find that, although these solution concepts are very different, one may just appear as a first order Taylor series approximation of the other, in certain cases. This may be good news for the Nash solution, or for the equilibrium allocation, all depending upon one’s point of view. Our model also allows us to readily identify some properties of the equilibrium allocation not be shared by the bargaining solution, and vice versa, related to both risk aversions and correlations.

Suggested Citation

  • Aase, Knut K., 2008. "The Nash Bargaining Solution vs. Equilibrium in a Reinsurance Syndicate," Discussion Papers 2008/5, Norwegian School of Economics, Department of Business and Management Science.
    • Handle: RePEc:hhs:nhhfms:2008_005
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    File URL: http://hdl.handle.net/11250/164118
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    References listed on IDEAS

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    1. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    2. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    3. Roth, Alvin E., 1977. "Independence of irrelevant alternatives, and solutions to Nash's bargaining problem," Journal of Economic Theory, Elsevier, vol. 16(2), pages 247-251, December.
    4. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
    5. Baton, Bernard & Lemaire, Jean, 1981. "The Bargaining Set of a Reinsurance Market," ASTIN Bulletin, Cambridge University Press, vol. 12(2), pages 101-114, December.
    6. Baton, Bernard & Lemaire, Jean, 1981. "The Core of a Reinsurance Market," ASTIN Bulletin, Cambridge University Press, vol. 12(1), pages 57-71, June.
    7. Roth, Alvin E & Rothblum, Uriel G, 1982. "Risk Aversion and Nash's Solution for Bargaining Games with Risky Outcomes," Econometrica, Econometric Society, vol. 50(3), pages 639-647, May.
    8. Borch, Karl, 1960. "Reciprocal Reinsurance Treaties," ASTIN Bulletin, Cambridge University Press, vol. 1(4), pages 170-191, December.
    9. Aase, Knut K., 1993. "Equilibrium in a Reinsurance Syndicate; Existence, Uniqueness and Characterization," ASTIN Bulletin, Cambridge University Press, vol. 23(2), pages 185-211, November.
    10. John Pratt, 2007. "Fair (and not so fair) division," Journal of Risk and Uncertainty, Springer, vol. 35(3), pages 203-236, December.
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    Cited by:

    1. Chen, Yanhong & Cheung, Ka Chun & Zhang, Yiying, 2024. "Bowley solution under the reinsurer's default risk," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 36-61.
    2. Liyuan Lin & Fangda Liu & Jingzhen Liu abd Luyang Yu, 2023. "The optimal reinsurance strategy with price-competition between two reinsurers," Papers 2305.00509, arXiv.org.

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    More about this item

    Keywords

    Nash’s Bargaining Solution; Equilibrium; Pareto Optimal Risk Exchange; Reinsurance Treaties; Uncertainty; Risk Aversion; Correlations; Multinormal Universe;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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