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Existence and Uniqueness of Equilibrium in a Reinsurance Syndicate


  • Aase, Knut K.

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


In this paper we consider a reinsurance syndicate, assuming that Pareto optimal allocations exist. Under a continuity assumption on preferences, we show that a competitive equilibrium exists and is unique. Our conditions allow for risks that are not bounded, and we show that the most standard models satisfy our set of sufficient conditions, which are thus not too restrictive. Our approach is to transform the analysis from an infinite dimensional to a finite dimensional setting.

Suggested Citation

  • Aase, Knut K., 2008. "Existence and Uniqueness of Equilibrium in a Reinsurance Syndicate," Discussion Papers 2008/13, Norwegian School of Economics, Department of Business and Management Science.
  • Handle: RePEc:hhs:nhhfms:2008_013

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    References listed on IDEAS

    1. Dana, Rose Anne, 1993. "Existence and Uniqueness of Equilibria When Preferences Are Additively Separable," Econometrica, Econometric Society, vol. 61(4), pages 953-957, July.
    2. Gerber, Hans U., 1978. "Pareto-Optimal Risk Exchanges and Related Decision Problems," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 10(01), pages 25-33, May.
    3. Aase, Knut K., 1993. "Equilibrium in a Reinsurance Syndicate; Existence, Uniqueness and Characterization," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 23(02), pages 185-211, November.
    4. Mas-Colell, Andreu & Zame, William R., 1991. "Equilibrium theory in infinite dimensional spaces," Handbook of Mathematical Economics,in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 34, pages 1835-1898 Elsevier.
    5. Araujo, A. & Monteiro, P. K., 1989. "Equilibrium without uniform conditions," Journal of Economic Theory, Elsevier, vol. 48(2), pages 416-427, August.
    6. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
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    More about this item


    Existence of equilibrium; uniqueness of equilibrium; Pareto optimality; reinsurance model; syndicate theory; risk tolerance; exchange economy; probability distributions; Walras’ law;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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