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

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  • 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)

Abstract

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

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Related research

Keywords: Overlapping sets of priors; collective absence of arbitrage; equilibria with short-selling; risk sharing; measures of risk.;

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  1. David Heath & Hyejin Ku, 2004. "Pareto Equilibria with coherent measures of risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 14(2), pages 163-172.
  2. Dov Samet, 1997. "Common Priors and Separation of Convex Sets," Game Theory and Information, EconWPA 9701002, EconWPA.
  3. 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.
  4. Hart, Oliver D., 1974. "On the existence of equilibrium in a securities model," Journal of Economic Theory, Elsevier, Elsevier, vol. 9(3), pages 293-311, November.
  5. Green, Jerry R, 1973. "Temporary General Equilibrium in a Sequential Trading Model with Spot and Futures Transactions," Econometrica, Econometric Society, Econometric Society, vol. 41(6), pages 1103-23, November.
  6. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 55(6), pages 1403-18, November.
  7. Burgert Christian & Rüschendorf Ludger, 2006. "On the optimal risk allocation problem," Statistics & Risk Modeling, De Gruyter, De Gruyter, vol. 24(1/2006), pages 19, July.
  8. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(3), pages 203-228.
  9. Nielsen, Lars Tyge, 1989. "Asset Market Equilibrium with Short-Selling," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 56(3), pages 467-73, July.
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Cited by:
  1. Rose-Anne Dana & Cuong Le Van, 2010. "Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers), HAL halshs-00470670, HAL.
  2. Stefano Bosi & Patrice Fontaine & Cuong Le Van, 2013. "Equilibrium existence in the international asset and good markets," Working Papers, Development and Policies Research Center (DEPOCEN), Vietnam 16, Development and Policies Research Center (DEPOCEN), Vietnam.
  3. Guillaume Carlier & Rose-Anne Dana, 2013. "Pareto optima and equilibria when preferences are incompletely known," Post-Print, HAL hal-00661903, HAL.
  4. G. Carlier & R.-A. Dana, 2014. "Pareto optima and equilibria when preferences are incompletely known," Working Papers, Department of Research, Ipag Business School 2014-060, Department of Research, Ipag Business School.
  5. repec:ipg:wpaper:3 is not listed on IDEAS

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