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Arbitrage and asset market equilibrium in infinite dimensional economies with short-selling and risk-averse expected utilities

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  • Thai Ha-Huy
  • Cuong Le Van
  • Manh-Hung Nguyen

Abstract

We consider a model with an inffnite number of states of nature, von Neumann - Morgenstern utilities, where agents have different probabil- ity beliefs and where short sells are allowed. We show that no-arbitrage conditions, deffned for ffnite dimensional asset markets models, are not sufficient to ensure existence of equilibrium in presence of an inffnite num- ber of states of nature. However, if the individually rational utility set U is compact, we obtain an equilibrium. We give conditions which imply the compactness of U. We give examples of non-existence of equilibrium when these conditions do not hold.

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Bibliographic Info

Paper provided by Department of Research, Ipag Business School in its series Working Papers with number 2014-100.

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Length: 23 pages
Date of creation: 25 Feb 2014
Date of revision:
Handle: RePEc:ipg:wpaper:2014-100

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Keywords: asset market equilibrium; individually rational attainable al- locations; individually rational utility set; no-arbitrage prices; no-arbitrage condition.;

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  1. Cheng, Harrison H. C., 1991. "Asset market equilibrium in infinite dimensional complete markets," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 137-152.
  2. Dana, R.A. & Le Van, C., 1996. "Asset Equilibria in "L" Spaces with Complete Markets: A Duality Approach," Papers, Toulouse - GREMAQ 95.388, Toulouse - GREMAQ.
  3. Brown, D.J. & Werner, J., 1992. "Arbitrage and Existence of Equilibrium in Finite Asset Markets," Papers, Stanford - Institute for Thoretical Economics 43, Stanford - Institute for Thoretical Economics.
  4. 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.
  5. PageJr., Frank H. & Wooders, Myrna H. & Monteiro, Paulo K., 2000. "Inconsequential arbitrage," Journal of Mathematical Economics, Elsevier, vol. 34(4), pages 439-469, December.
  6. Geistdoerfer-Florenzano, Monique, 1982. "The gale-nikaido-debreu lemma and the existence of transitive equilibrium with or without the free-disposal assumption," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 113-134, January.
  7. repec:hal:journl:halshs-00470670 is not listed on IDEAS
  8. Allouch, Nizar & Le Van, Cuong & Page, Jr. Frank H., 2001. "The geometry of arbitrage and the existence of competitive equilibrium," The Warwick Economics Research Paper Series (TWERPS) 598, University of Warwick, Department of Economics.
  9. Chichilnisky Graciela & Heal Geoffrey M., 1993. "Competitive Equilibrium in Sobolev Spaces without Bounds on Short Sales," Journal of Economic Theory, Elsevier, vol. 59(2), pages 364-384, April.
  10. 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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  12. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 55(6), pages 1403-18, November.
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Cited by:
  1. Ilyes Abid & Khaled Guesmi & Olfa Kaabia & Duc Khuong Nguyen, 2014. "Financial Crises and Contagion Effects between the US and OECD Equity Markets," Working Papers 2014-451, Department of Research, Ipag Business School.
  2. Olfa Bouasker & Jean-Luc Prigent, 2014. "Corporate Investment Choice and Exchange Option between Production Functions," Working Papers 2014-511, Department of Research, Ipag Business School.
  3. Frederic Teulon, 2014. "A propos de Walras et de la théorie de l’équilibre général," Working Papers 2014-556, Department of Research, Ipag Business School.
  4. Omar Masood & Shazaib Butt & Syed Alamdar Ali & Frederic Teulon & Olivier Levyne, 2014. "Sensitivity Analysis of Domestic Credit to Private Sector in Pakistan: A Variable Replacement Approach Applied with Con-integration," Working Papers 2014-452, Department of Research, Ipag Business School.
  5. Furkan Emirmahmutoglu & Nicholas Apergis & Beatrice D. Simo-Kengne & Tsangyao Chang & Rangan Gupta, 2014. "Causal relationship between asset prices and output in the US: Evidence from state-level panel Granger causality test," Working Papers 201411, University of Pretoria, Department of Economics.
  6. Frederic Teulon, 2014. "Ce que nous devons à Paul Samuelson (1915-2009)," Working Papers 2014-560, Department of Research, Ipag Business School.
  7. Frederic Teulon, 2014. "George Stigler : combat pour la déréglementation," Working Papers 2014-570, Department of Research, Ipag Business School.
  8. Naceur Naguez & Jean-Luc Prigent, 2014. "Kappa Performance Measures with Johnson Distributions," Working Papers 2014-510, Department of Research, Ipag Business School.

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