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Arbitrage and Existence of Equilibrium in Infinite Asset Markets

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Author Info
Brown, Donald J
Werner, Jan

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Abstract

This paper develops a framework for a general equilibrium analysis of asset markets when the number of assets is infinite. The authors show that an equilibrium exists if there is a price system under which no investor has an arbitrage opportunity. For the case of infinite asset markets, they introduce a concept of sequential arbitrage opportunity that is a sequence of portfolios which increases an investor's utility indefinitely and has zero price in the limit. The authors show that a sequential arbitrage opportunity and an arbitrage portfolio are equivalent concepts in finite markets but not in their infinite counterpart. Copyright 1995 by The Review of Economic Studies Limited.

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Publisher Info
Article provided by Blackwell Publishing in its journal Review of Economic Studies.

Volume (Year): 62 (1995)
Issue (Month): 1 (January)
Pages: 101-14
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Handle: RePEc:bla:restud:v:62:y:1995:i:1:p:101-14

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  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. [Downloadable!] (restricted)
  2. Chichilniski, G. & Heal, G., 1991. "Competitive Equilibrium in Sobolev Spaces with Unbounded Short Sales," Discussion Papers 1991_32, Columbia University, Department of Economics.
    Other versions:
  3. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-304, September. [Downloadable!] (restricted)
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  4. Connor, Gregory, 1984. "A unified beta pricing theory," Journal of Economic Theory, Elsevier, vol. 34(1), pages 13-31, October. [Downloadable!] (restricted)
  5. Nielsen, Lars Tyge, 1990. "Existence of equilibrium in CAPM," Journal of Economic Theory, Elsevier, vol. 52(1), pages 223-231, October. [Downloadable!] (restricted)
  6. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-18, November. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. Kreps, David M., 1981. "Arbitrage and equilibrium in economies with infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 15-35, March. [Downloadable!] (restricted)
  9. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
  11. Hammond, Peter J., 1983. "Overlapping expectations and Hart's conditions for equilibrium in a securities model," Journal of Economic Theory, Elsevier, vol. 31(1), pages 170-175, October. [Downloadable!] (restricted)
  12. Nielsen, Lars Tyge, 1989. "Asset Market Equilibrium with Short-Selling," Review of Economic Studies, Blackwell Publishing, vol. 56(3), pages 467-73, July. [Downloadable!] (restricted)
  13. Page, Frank Jr., 1987. "On equilibrium in Hart's securities exchange model," Journal of Economic Theory, Elsevier, vol. 41(2), pages 392-404, April. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Cuong Le Van & Frank H. Page & Myrna H. Wooders, 2007. "Risky Arbitrage, Asset Prices, and Externalities," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00102698_v1, HAL. [Downloadable!]
    Other versions:
  2. Rose-Anne Dana & Cuong Le Van, 2008. "Overlapping sets of priors and the existence ofefficient allocations and equilibria for risk measures," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00308530_v1, HAL. [Downloadable!]
  3. Nizar Allouch, 2000. "Edgeworth and Walras Equilibria of an Arbitrage-Free Exchange Economy," Econometric Society World Congress 2000 Contributed Papers 1901, Econometric Society. [Downloadable!]
    Other versions:
  4. Wassin Daher & V. Filipe Martins-da-Rocha & Yiannis Vailakis, 2005. "Asset market equilibrium with short-selling and differential information," Cahiers de la Maison des Sciences Economiques b05098, Université Panthéon-Sorbonne (Paris 1). [Downloadable!]
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