The geometry of arbitrage and the existence of competitive equilibrium
AbstractWe 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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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Mathematical Economics.
Volume (Year): 38 (2002)
Issue (Month): 4 (December)
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Web page: http://www.elsevier.com/locate/jmateco
Other versions of this item:
- 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.
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
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- Grandmont, Jean-Michel, 1977. "Temporary General Equilibrium Theory," Econometrica, Econometric Society, vol. 45(3), pages 535-72, April.
- Milne, Frank, 1976. "Default Risk in a General Equilibrium Asset Economy with Incomplete Markets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(3), pages 613-25, October.
- Nielsen, Lars Tyge, 1989. "Asset Market Equilibrium with Short-Selling," Review of Economic Studies, Wiley Blackwell, vol. 56(3), pages 467-73, July.
- Page Jr., Frank H. & Wooders, Myrna Holtz, 1996. "A necessary and sufficient condition for the compactness of individually rational and feasible outcomes and the existence of an equilibrium," Economics Letters, Elsevier, vol. 52(2), pages 153-162, August.
- Milne, Frank, 1980. "Short-Selling, Default Risk and the Existence of Equilibrium in a Securities Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(2), pages 255-67, June.
- Dana, R.-A. & Le Van, C. & Magnien, F., 1999.
"On the Different Notions of Arbitrage and Existence of Equilibrium,"
Papiers d'Economie MathÃÂ©matique et Applications
1999.34, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
- Dana, Rose-Anne & Le Van, Cuong & Magnien, Francois, 1999. "On the Different Notions of Arbitrage and Existence of Equilibrium," Journal of Economic Theory, Elsevier, vol. 87(1), pages 169-193, July.
- Dana, Rose-Anne & Le Van, Cuong & Magnien, François, 1996. "On the different notions of arbitrage and existence of equilibrium," CEPREMAP Working Papers (Couverture Orange) 9616, CEPREMAP.
- PageJr., Frank H. & Wooders, Myrna H. & Monteiro, Paulo K., 2000.
Journal of Mathematical Economics,
Elsevier, vol. 34(4), pages 439-469, December.
- Page, F.H.Jr. & Wooders, M.H. & Monteiro, P.K., 1999. "Inconsequential Arbitrage," The Warwick Economics Research Paper Series (TWERPS) 561, University of Warwick, Department of Economics.
- Allouch, Nizar, 2002. "An equilibrium existence result with short selling," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 81-94, April.
- Brown, Donald & Werner, Jan, 1993.
"Arbitrage and Existence of Equilibrium in Infinite Asset Markets,"
825, California Institute of Technology, Division of the Humanities and Social Sciences.
- Brown, Donald J & Werner, Jan, 1995. "Arbitrage and Existence of Equilibrium in Infinite Asset Markets," Review of Economic Studies, Wiley Blackwell, vol. 62(1), pages 101-14, January.
- Brown, D.J. & Werner, J., 1992. "Arbitrage and Existence of Equilibrium in Finite Asset Markets," Papers 43, Stanford - Institute for Thoretical Economics.
- Brown,Donald & Werner,Jan, 1991. "Arbitrage and existence of equilibrium in infinite asset markets," Discussion Paper Serie A 344, University of Bonn, Germany.
- 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.
- Kim, Chongmin, 1998. "Stochastic Dominance, Pareto Optimality, and Equilibrium Asset Pricing," Review of Economic Studies, Wiley Blackwell, vol. 65(2), pages 341-56, April.
- Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-18, November.
- 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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