Danilov, Vladimir and Koshovoy, Gleb and Page, Frank and Wooders, Myrna (2011): Existence of equilibrium with unbounded short sales: A new approach.
Download (251Kb) | Preview
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).
|Item Type:||MPRA Paper|
|Original Title:||Existence of equilibrium with unbounded short sales: A new approach|
|English Title:||Existence of equilibrium with unbounded short sales: A new approach|
|Keywords:||arbitrage; unbounded short sales; asset market models; sum of weakly preferred sets; existence of equilibrium|
|Subjects:||D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D53 - Financial Markets
D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D50 - General
D - Microeconomics > D4 - Market Structure and Pricing > D40 - General
|Depositing User:||Myrna Wooders|
|Date Deposited:||31. Mar 2012 22:35|
|Last Modified:||18. Feb 2013 12:09|
Allouch, N. (2002) An equilibrium existence result with short selling. Journal of Mathematical Economics 37, 81--94.
Allouch N., C. Le Van, and F.Page. (2002) The geometry of arbitrage and the existence of competitive equilibrium, Journal of Mathematical Economics 38, 373--391.
Dana R.-A., C.Le Van, and F.Magnien. (1997) General equilibrium in asset markets with or without short-selling. J. of Math. Analysis and Appl. 206, 567--588.
Dana, R.-A., C. Le Van, and F. Magnien (1999) On different notion of arbitrage and existence of equilibrium, Journal of Economic Theory 87, 169-193.
Danilov V.I. and G.A.Koshevoy. (1999) Separation of closed sets. mimeo. In Russian.
Florenzano, M. and C. Le Van (2001) Finite Dimensional Convexity and Optimization, Springer-Verlag, Berlin, Heidelberg, New York.
Grandmont, J.M. (1982) Temporary general equilibrium theory, Handbook of Mathematical Economics Volume II, North Holland.
Grandmont, J.M. (1977) Temporary general equilibrium theory, Econometrica 45, 535-572.
Green, J.R. (1973) Temporary General Equilibrium in a Sequential Trading Model with Spot and Futures Transactions, Econometrica 41, 1103-1123.
Hammond, P.J. (1983) Overlapping expectations and Hart's condition for equilibrium in a securities model, Journal of Economic Theory 31, 170-175.
Hart. O. (1974) On the existence of an equilibrium in a securities model. J. of Econ. Theory, 9, 293--311.
Ha-Huy, T. (2011) "Equilibre sur les marches financiers - Croissance optimale et bien-^etre social, Ph.D. Dissertation, under the supervision of C. Levan, Paris 1.
Milne, F. (1981) "Short-selling, default risk and the existence of equilibrium in a securities model," International Economic Review 21, 255-267.
Mirkil H. (1957) New characterization of polyhedral cones. Canad. J. Math., 9, 1--4.
Nielsen, L.T. (1989) Asset market equilibrium with short-selling, Review of Economic Studies 56. 467-474.
Page, F.H.Jr. (1987) On equilibrium in Hart's securities exchange model. J. of Econ. Theory. 41, 392--404.
Page, F.H. Jr., and M. Wooders (1996) A necessary and sufficient condition for compactness of individually rational and feasible outcomes and existence of an equilibrium. Economics Letters 52 (1996) 153-162.
Page, F.H.Jr., Wooders, M. and P.K.Monteiro. (2000). Inconsequential arbitrage. J. of Math. Economics 34, 439-469.
Rockafellar R.T. (1970) Convex Analysis. Princeton Univ. Press.
Werner J. (1987). Arbitrage and the existence of competitive equilibrium. Econometrica, 55, 1403--1418