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

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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 Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number b07068.

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Length: 20 pages
Date of creation: Jul 2007
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Handle: RePEc:mse:cesdoc:b07068

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

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  1. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-18, November.
  2. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  3. Samet, Dov, 1998. "Common Priors and Separation of Convex Sets," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 172-174, July.
  4. 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.
  5. Burgert Christian & Rüschendorf Ludger, 2006. "On the optimal risk allocation problem," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 19, July.
  6. David Heath & Hyejin Ku, 2004. "Pareto Equilibria with coherent measures of risk," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 163-172.
  7. 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.
  8. Nielsen, Lars Tyge, 1989. "Asset Market Equilibrium with Short-Selling," Review of Economic Studies, Wiley Blackwell, vol. 56(3), pages 467-73, July.
  9. 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.
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Cited by:
  1. Le Van, Cuong & Dana, Rose-Anne, 2010. "Overlapping Risk Adjusted Sets of Priors and the Existence of Efficient Allocations and Equilibria with Short-Selling," Economics Papers from University Paris Dauphine 123456789/5045, Paris Dauphine University.
  2. Guillaume Carlier & Rose-Anne Dana, 2013. "Pareto optima and equilibria when preferences are incompletely known," Post-Print hal-00661903, HAL.
  3. Stefano Bosi & Patrice Fontaine & Cuong Le Van, 2013. "Equilibrium existence in the international asset and good markets," Working Papers 2013-003, Department of Research, Ipag Business School.
  4. G. Carlier & R.-A. Dana, 2014. "Pareto optima and equilibria when preferences are incompletely known," Working Papers 2014-060, Department of Research, Ipag Business School.

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