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The Core of a Reinsurance Market

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  • Baton, Bernard
  • Lemaire, Jean

Abstract

In a series of celebrated papers, K. Borch characterized the set of the Pareto-optimal risk exchange treaties in a reinsurance market. However, the Pareto-optimality and the individual rationality conditions, considered by Borch, do not preclude the possibility that a coalition of companies might be better off by seceding from the whole group. In this paper, we introduce this collective rationality condition and characterize the core of this game without transferable utilities in the important special case of exponential utilities. The mathematical conditions we obtain can be interpreted in terms of insurance premiums, calculated by means of the zero-utility premium calculation principle. We then show that the core is always non-void and conclude by an example.

Suggested Citation

  • Baton, Bernard & Lemaire, Jean, 1981. "The Core of a Reinsurance Market," ASTIN Bulletin, Cambridge University Press, vol. 12(1), pages 57-71, June.
    • Handle: RePEc:cup:astinb:v:12:y:1981:i:01:p:57-71_00
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    Citations

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    Cited by:

    1. Jiahua Zhang & Shu-Cherng Fang & Yifan Xu, 2018. "Inventory centralization with risk-averse newsvendors," Annals of Operations Research, Springer, vol. 268(1), pages 215-237, September.
    2. Jaramillo, Fernando & Kempf, Hubert & Moizeau, Fabien, 2015. "Heterogeneity and the formation of risk-sharing coalitions," Journal of Development Economics, Elsevier, vol. 114(C), pages 79-96.
    3. Sjur Didrik Flåm, 2002. "Pooling, Pricing and Trading of Risks," CESifo Working Paper Series 672, CESifo.
    4. Flåm, Sjur Didrik, 2002. "Full Coverage for Minor, Recurrent Losses?," Working Papers in Economics 10/02, University of Bergen, Department of Economics.
    5. Asimit, Vali & Boonen, Tim J., 2018. "Insurance with multiple insurers: A game-theoretic approach," European Journal of Operational Research, Elsevier, vol. 267(2), pages 778-790.
    6. Knut Aase, 2009. "The Nash bargaining solution vs. equilibrium in a reinsurance syndicate," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2009(3), pages 219-238.
    7. Borglin, Anders & Flåm, Sjur, 2007. "Risk Exchange as a Market or Production Game," Working Papers 2007:16, Lund University, Department of Economics.
    8. Powers, Michael R. & Shubik, Martin, 2001. "Toward a theory of reinsurance and retrocession," Insurance: Mathematics and Economics, Elsevier, vol. 29(2), pages 271-290, October.
    9. Sjur Flåm, 2009. "Pooling, pricing and trading of risks," Annals of Operations Research, Springer, vol. 165(1), pages 145-160, January.
    10. Powers, Michael R. & Shubik, Martin, 1998. "On the tradeoff between the law of large numbers and oligopoly in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 23(2), pages 141-156, November.
    11. Michael Powers & Martin Shubik & Shun Yao, 1998. "Insurance market games: Scale effects and public policy," Journal of Economics, Springer, vol. 67(2), pages 109-134, June.
    12. Sjur Didrik Flåm, 2004. "Social Insurance of Short Spell Sickness," Nordic Journal of Political Economy, Nordic Journal of Political Economy, vol. 30, pages 79-90.
    13. Aase, Knut K., 2006. "Optimal Risk-Sharing and Deductables in Insurance," Discussion Papers 2006/24, Norwegian School of Economics, Department of Business and Management Science.
    14. Zhi Chen & Weijun Xie, 2021. "Sharing the value‐at‐risk under distributional ambiguity," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 531-559, January.

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