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Overlapping sets of priors and the existence of efficient allocations and equilibria for risk measures

  • Rose-Anne Dana

    ()

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris IX - Paris Dauphine)

  • Cuong Le Van

    ()

    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)

The overlapping expectations and the collective absence of arbitrage conditions introduced in the economic literature to insure existence of Pareto optima and equilibria when short-selling is allowed and investors hold a single belief about future returns, is reconsidered. Investors use measures of risk. The overlapping sets of priors and the Pareto equilibrium conditions introduced by Heath and Ku for coherent risk measures are reinterpreted as a weak no-arbitrage and a weak collective absence of arbitrage conditions and shown to imply existence of Pareto optima and Arrow Debreu equilibria.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00188761.

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Date of creation: Jul 2007
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Handle: RePEc:hal:cesptp:halshs-00188761
Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00188761
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  1. Allouch, Nizar & Le Van, Cuong & Page, Frank Jr., 2002. "The geometry of arbitrage and the existence of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 38(4), pages 373-391, December.
  2. Samet, Dov, 1998. "Common Priors and Separation of Convex Sets," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 172-174, July.
  3. Green, Jerry R, 1973. "Temporary General Equilibrium in a Sequential Trading Model with Spot and Futures Transactions," Econometrica, Econometric Society, vol. 41(6), pages 1103-23, November.
  4. Burgert Christian & Rüschendorf Ludger, 2006. "On the optimal risk allocation problem," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 19, July.
  5. Hart, Oliver D., 1974. "On the existence of equilibrium in a securities model," Journal of Economic Theory, Elsevier, vol. 9(3), pages 293-311, November.
  6. Nielsen, Lars Tyge, 1989. "Asset Market Equilibrium with Short-Selling," Review of Economic Studies, Wiley Blackwell, vol. 56(3), pages 467-73, July.
  7. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  8. David Heath & Hyejin Ku, 2004. "Pareto Equilibria with coherent measures of risk," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 163-172.
  9. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-18, November.
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