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Equilibrium in a Reinsurance Syndicate; Existence, Uniqueness and Characterization

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  • Aase, Knut K.

Abstract

This paper attempts to give an overview of the pricing of risks in a pure exchange economy, where trade takes place at time zero and where uncertainty is revealed at time one. An economic equilibrium model under uncertainty is formulated, where conditions characterizing a Pareto optimal exchange equilibrium are derived. We present two sets of sufficient conditions for the existence of an equilibrium, and demonstrate how equilibria can be characterized through several examples. Uniqueness of equilibrium is also discussed. Special attention is given to the principal components that the premiums in a reinsurance market must depend upon. We also apply the general theory to the risk exchange problem between a policyholder and an insurer, and in particular we compute market premiums of the resulting optimal contracts. It is emphasized throughout how the formulation of a competitive equilibrium, rather than merely a general risk exchange formulation, is of particular interest in deriving a well-defined and unique set of equilibrium premiums in an insurance market. The theory is put into a framework which is fruitful for extensions beyond the one-period case.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:astinb:v:23:y:1993:i:02:p:185-211_01
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    Cited by:

    1. Denuit, M. & Robert, C.Y., 2020. "Ultimate behavior of conditional mean risk sharing for independent compound Panjer-Katz sums with gamma and Pareto severities," LIDAM Discussion Papers ISBA 2020014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. 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.
    3. Knut K. Aase, 2022. "Optimal Risk Sharing in Society," Mathematics, MDPI, vol. 10(1), pages 1-31, January.
    4. Andreas Tsanakas & Evangelia Desli, 2005. "Measurement and Pricing of Risk in Insurance Markets," Risk Analysis, John Wiley & Sons, vol. 25(6), pages 1653-1668, December.
    5. Knut K. Aase, 2007. "Equilibrium in Marine Mutual Insurance Markets with Convex Operating Costs," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(1), pages 239-268, March.
    6. Maxim Bichuch & Zachary Feinstein, 2020. "Endogenous inverse demand functions," Papers 2012.08002, arXiv.org, revised Apr 2022.
    7. Christian Gollier, 2005. "Some Aspects of the Economics of Catastrophe Risk Insurance," CESifo Working Paper Series 1409, CESifo.
    8. 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.
    9. Borglin, Anders & Flåm, Sjur, 2007. "Risk Exchange as a Market or Production Game," Working Papers 2007:16, Lund University, Department of Economics.
    10. Boonen, Tim J. & Pantelous, Athanasios A. & Wu, Renchao, 2018. "Non-cooperative dynamic games for general insurance markets," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 123-135.
    11. De Waegenaere, Anja & Kast, Robert & Lapied, Andre, 2003. "Choquet pricing and equilibrium," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 359-370, July.
    12. Iwaki, Hideki & Kijima, Masaaki & Morimoto, Yuji, 2001. "An economic premium principle in a multiperiod economy," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 325-339, June.
    13. Aase, Knut K., 2010. "Existence and Uniqueness of Equilibrium in a Reinsurance Syndicate," ASTIN Bulletin, Cambridge University Press, vol. 40(2), pages 491-517, November.
    14. Masaaki Kijima & Akihisa Tamura, 2014. "Buhlmann’s Economic Premium Principle in The Presence of Transaction Costs," KIER Working Papers 893, Kyoto University, Institute of Economic Research.
    15. Paulsen, Jostein, 1995. "Optimal per claim deductibility in insurance with the possibility of risky investments," Insurance: Mathematics and Economics, Elsevier, vol. 17(2), pages 133-147, October.
    16. Rodrigo S. Targino & Gareth W. Peters & Georgy Sofronov & Pavel V. Shevchenko, 2017. "Optimal Exercise Strategies for Operational Risk Insurance via Multiple Stopping Times," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 487-518, June.
    17. Aase, Knut K., 2007. "Wealth Effects on Demand for Insurance," Discussion Papers 2007/6, Norwegian School of Economics, Department of Business and Management Science.
    18. Gerber, Hans U. & Shiu, Elias S. W., 1996. "Actuarial bridges to dynamic hedging and option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 18(3), pages 183-218, November.
    19. Takuya Nakaizumi & Satoru Yano, 2017. "The soft budget constraint problem and hard budget solution of outward reinsurance markets for providing insurance to local economy against natural disaster," Asia-Pacific Journal of Regional Science, Springer, vol. 1(2), pages 625-637, October.
    20. Claire Mouminoux & Christophe Dutang & Stéphane Loisel & Hansjoerg Albrecher, 2022. "On a Markovian Game Model for Competitive Insurance Pricing," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1061-1091, June.
    21. Dijkstra, Theo K. & Yao, Yong, 2002. "Moment generating function approach to pricing interest rate and foreign exchange rate claims," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 163-178, October.

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