Existence of equilibrium with unbounded short sales: a new approach
We introduce a new approach to showing existence of equilibrium in models of economies with unbounded short sales. Inspired by the pioneering works of Hart (1974) on asset market models, Grandmont (1977) on temporary economic equilibrium, and of Werner (1987) on general equilibrium exchange economies, all papers known to us stating conditions for existence of equilibrium with unbounded short sales place conditions on recession cones of agents' preferred sets or, more recently, require compactness of the utility possibilities set. In contrast, in this paper, we place conditions on the preferred sets themselves. Roughly, our condition is that the sum of the weakly preferred sets is a closed set. We demonstrate that our condition implies existence of equilibrium. In addition to our main theorem, we present two theorems showing cases to which our main theorem can we applied. We also relate our condition to the classic condition of Hart (1974).
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- Allouch, Nizar, 2002. "An equilibrium existence result with short selling," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 81-94, April.
- 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.
- Allouch, Nizar & Le Van, Cuong & Page, Frank Jr., 2002. "The geometry of arbitrage and the existence of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 38(4), pages 373-391, December.
- 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.
- Grandmont, Jean-Michel, 1977.
"Temporary General Equilibrium Theory,"
Econometric Society, vol. 45(3), pages 535-72, April.
- Dana, Rose-Anne & Le Van, Cuong & Magnien, François, 1999.
"On the Different Notions of Arbitrage and Existence of Equilibrium,"
Economics Papers from University Paris Dauphine
123456789/6228, Paris Dauphine University.
- 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.
- 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).
- 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.
- Nielsen, Lars Tyge, 1989. "Asset Market Equilibrium with Short-Selling," Review of Economic Studies, Wiley Blackwell, vol. 56(3), pages 467-73, July.
- Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-18, November.
- 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.
- 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.
- 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.
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