The geometry of arbitrage and the existence of competitive equilibrium
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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- Page, F.H.Jr. & Wooders, M.H. & Monteiro, P.K., 1999.
The Warwick Economics Research Paper Series (TWERPS)
561, University of Warwick, Department of Economics.
- Grandmont, Jean-Michel, 1977.
"Temporary General Equilibrium Theory,"
Econometric Society, vol. 45(3), pages 535-572, April.
- Grandmont, Jean-Michel, 1972. "Continuity properties of a von Neumann-Morgenstern utility," Journal of Economic Theory, Elsevier, vol. 4(1), pages 45-57, February.
- Nizar Allouch & Cuong Le Van & Frank H. Page, Jr., 2004.
"Arbitrage, Equilibrium, and Nonsatiation,"
512, Queen Mary University of London, School of Economics and Finance.
- 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.
- Green, Jerry R, 1973. "Temporary General Equilibrium in a Sequential Trading Model with Spot and Futures Transactions," Econometrica, Econometric Society, vol. 41(6), pages 1103-1123, November.
- 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.
- 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, 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.
- Dana, R.-A. & Le Van, C. & Magnien, F., 1999.
"On the Different Notions of Arbitrage and Existence of Equilibrium,"
Papiers d'Economie MathÃ©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.
- Donald J. Brown & Jan Werner, 1995.
"Arbitrage and Existence of Equilibrium in Infinite Asset Markets,"
Review of Economic Studies,
Oxford University Press, vol. 62(1), pages 101-114.
- Brown,Donald & Werner,Jan, 1991. "Arbitrage and existence of equilibrium in infinite asset markets," Discussion Paper Serie A 344, University of Bonn, Germany.
- Brown, Donald & Werner, Jan, 1993. "Arbitrage and Existence of Equilibrium in Infinite Asset Markets," Working Papers 825, California Institute of Technology, Division of the Humanities and Social Sciences.
- Brown, D.J. & Werner, J., 1992. "Arbitrage and Existence of Equilibrium in Finite Asset Markets," Papers 43, Stanford - Institute for Thoretical Economics.
- repec:dau:papers:123456789/6228 is not listed on IDEAS
- Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-1418, November.
- Allouch, N., 2000. "Equilibrium and Bounded Arbitrage," Papiers d'Economie MathÃ©matique et Applications 2000.78, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
- 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.
- Lars Tyge Nielsen, 1989. "Asset Market Equilibrium with Short-Selling," Review of Economic Studies, Oxford University Press, vol. 56(3), pages 467-473.
- Chongmin Kim, 1998. "Stochastic Dominance, Pareto Optimality, and Equilibrium Asset Pricing," Review of Economic Studies, Oxford University Press, vol. 65(2), pages 341-356.
- Page, Frank Jr., 1987. "On equilibrium in Hart's securities exchange model," Journal of Economic Theory, Elsevier, vol. 41(2), pages 392-404, April.
- Allouch, Nizar, 2002. "An equilibrium existence result with short selling," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 81-94, April.
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