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The geometry of arbitrage and the existence of competitive equilibrium

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Author Info
Allouch, Nizar
Le Van, Cuong
Page, Jr. Frank H.

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Abstract

We present the basic geometry of arbitrage and use this basic geometry to shed new light on the relationships between various noarbitrage conditions found in the literature. For example, under very mild conditions of Hart (1974) and Werner (1987) are equivalent and imply the compactness of the set of utility possibilities. Moreover, we show that if agents' sets of useless net trades are linearly independent, then the Hart-Werner conditions are equilivent to the stronger condition of no-unbounded-arbitrage due to Page (1987) - and, in turn, all are equilivalent to compactness of the set of rational allocations. We also consider the problem of existence of equilibrium. We show, for example, that under a uniformity condition on preferences weaker than Werner's uniformity condition, the Hart-Werner no-arbitrage conditions are sufficient for existence. With an additional condition of weak no half lines - a condition weaker than Werner's no-half lines condition - we show that the Hart-Werner conditions are both necessary and sufficient for existence.

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File URL: http://www2.warwick.ac.uk/fac/soc/economics/research/workingpapers/publications/twerp598.pdf
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Paper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 598.

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Length: 23 pages
Date of creation: 2001
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Handle: RePEc:wrk:warwec:598

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Related research
Keywords: ARBITRAGE ; COMPETITIVE EQUILIBRIUM ; RECESSION CONES;

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Find related papers by JEL classification:
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

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  1. Manh-Hung Nguyen & Thai Ha-Huy, 2008. "No unbounded arbitrage, weak no market arbitrage and no arbitrage price system conditions: The circular results," THEMA Working Papers 2008-08, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise. [Downloadable!]
    Other versions:
  2. LE VAN, Cuong & BA MINH, Nguyen, 2004. "No-arbitrage condition and existence of equilibrium with dividends," CORE Discussion Papers 2004034, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
  3. Martins-da-Rocha, V. F. & Monteiro, Paulo Klinger, 2007. "Unbounded exchange economies with satiation: how far can we go?," Economics Working Papers (Ensaios Economicos da EPGE) 646, Graduate School of Economics, Getulio Vargas Foundation (Brazil). [Downloadable!]
    Other versions:
  4. Nizar Allouch & Cuong Le Van, 2008. "Walras and dividends equilibrium with possibly satiated consumers," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00101189_v2, HAL. [Downloadable!]
    Other versions:
  5. Cuong Le Van & Nguyen Ba Minh, 2004. "No-arbitrage condition and existence of equilibrium with dividends," Cahiers de la Maison des Sciences Economiques b04058, Université Panthéon-Sorbonne (Paris 1). [Downloadable!]
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  6. Allouch, Nizar & Van, Cuong Le & Page Jr. Frank H., 2002. "Arbitrage, Equilibrium And Nonsatiation," The Warwick Economics Research Paper Series (TWERPS) 637, University of Warwick, Department of Economics. [Downloadable!]
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  7. 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!]
  8. Thai Ha Huy & Cuong Le Van & Manh Hung NGUYEN, 2008. "No arbitrage condition and existence of equilibrium in infinite or finite dimension with expected risk averse utilities," Working Papers 08.27.271, LERNA, University of Toulouse. [Downloadable!]
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  9. Cuong Le Van & Nguyen Ba Minh, 2007. "No-arbitrage condition and existence of equilibrium with dividends," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00101177_v1, HAL. [Downloadable!]
  10. Nizar Allouch & Cuong Le Van & Frank H. Page, 2006. "Arbitrage and equilibrium in unbounded exchange economies with satiation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00096040_v1, HAL. [Downloadable!]
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  11. Nizar Allouch & Monique Florenzano, 2004. "Edgeworth and Walras equilibria of an arbitrage-free exchange economy," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00086096_v1, HAL. [Downloadable!]
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  12. NGUYEN Manh-Hung & HA-HUY Thai, 2008. "No unbounded arbitrage, weak no market arbitrage and no arbitrage price system conditions; Equivalent conditions," Working Papers 08.23.267, LERNA, University of Toulouse. [Downloadable!]
  13. 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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