Arbitrage, equilibrium and nonsatiation
Allouch, Nizar, Le, Van Cuong and Page, Frank H. (2002) Arbitrage, equilibrium and nonsatiation. Working Paper. University of Warwick, Department of Economics, Coventry.
WRAP_Allouch_twerp637.pdf - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Official URL: http://www2.warwick.ac.uk/fac/soc/economics/resear...
In his seminal paper on arbitrage and competitive equilibrium in unbounded exchange economies, Werner (Econometrica, 1987)proved the existence of a competitive equilibrium, under a price no-arbitrage condition, without assuming either local or global nonsatiation. Werner's existence result contrasts sharply with classical existence results for bounded exchange economies which require, at minimum, global nonsatiation at rational allocations. Why do un-bounded exchange economies admit existence without local or global nonsatiation? This question is the focus of our paper. We make two main contributions to the theory of arbitrage and competitive equilibrium. First, we show that, in general, in unbounded exchange economies (for example, asset exchange economies allowing short sales), even if some agents' preferences are satiated, the absence of arbitrage is sufficient for the existence of competitive equilibria, as long as each agent who is satiated has a nonempty set of useful net trades - that is, as long as agents' preferences satisfy weak nonsatiation. Second, we provide a new approach to proving existence in unbounded exchange economies. The key step in our new approach is to transform the original economy to an economy satisfying global nonsatiation such that all equilibria of the transformed economy are equilibria of the original economy. What our approach makes clear is that it is precisely the condition of weak nonsatiation - a condition considerably weaker than local or global nonsatiation - that makes possible this transformation. Moreover, as we show via examples, without weak nonsatiation, existence fails.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||H Social Sciences > HG Finance|
|Divisions:||Faculty of Social Sciences > Economics|
|Library of Congress Subject Headings (LCSH):||Arbitrage, Equilibrium (Economics), Asset-backed financing, Recessions|
|Series Name:||Warwick economic research papers|
|Publisher:||University of Warwick, Department of Economics|
|Place of Publication:||Coventry|
|Number of Pages:||27|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|Description:||July, 2001; current version, January, 2002|
|References:|| Allouch N., An equilibrium existence result with short selling, Journal of Mathematical Economics, forthcoming, (2002).  Allouch N., Le Van, C., Page, F.H.Jr., The geometry of arbitrage and the existence of competitive equilibrium,Warwick Economic Research Papers, No 598, Department of Economics, University of Warwick, (2001).  Bergstrom, T. C., How to discard `free disposability' - at no cost, Journal of Mathematical Economics 3, 131-134 (1976).  Dana, R.-A., Le Van, C., Magnien F., On the di�erent notions of arbitrage and existence of equilibrium, Journal of Economic Theory 86, 169-193 (1999).  Debreu, G., Theory of Value, John Wiley and Sons, New-York, (1959).  Florenzano, M., Le Van, C., A note on Gale-Nikaido-Debreu lemma and the existence of general equilibrium, Economics Letters 32, 107-110, (1986).  Gale, D., Mas-Colell, A., An equilibrium existence theorem for a general model without ordered preferences, Journal of Mathematical Economics 2, 9-15 (1975).  Geistdoerfer-Florenzano, M., The Gale-Nikaido-Debreu lemma and the existence of transitive equilibrium with or without the free-disposal assumption, Journal of Mathematical Economics 9, 113-134 (1982).  Grandmont, J.M., On the Temporary Competitive Equilibrium, Working Paper, No. 305, Center for Research in Management Science, University of California, Berkeley, August (1970).  Grandmont, J.M., Continuity Properties of a von Neumann-Morgenstern Utility, Journal of Economic Theory 5, 45-57, (1972).  Grandmont, J.M., Temporary general equilibrium theory, Econometrica 45, 535-572, (1977).  Green, J.R., Temporary general equilibrium in a sequential trading model with spot and futures transactions, Econometrica 41, 1103-1124, (1973).  Hammond, P.J., Overlapping expectations and Hart's condition for equilibrium in a securities model, Journal of Economics Theory 31, 170-175 (1983).  Hart, O., On the existence of an equilibrium in a securities model, Journal of Economic Theory 9, 293-311 (1974).  Kim, C., Stochastic dominance, Pareto optimality and equilibrium asset pricing, Review of Economic Studies 65, 341-356 (1998).  Milne, F., Default risk in a general equilibrium asset economy with incomplete market, International Economic Review 17, 613-625 (1976).  Milne, F., Short selling, default risk and the existence of equilibrium in a securities model, International Economic Review 21, 255-267 (1980).  Nielsen, L.T., Asset market equilibrium with short selling, Review of Economic Studies 56, 467-474 (1989)  Page, F.H.Jr., On equilibrium in Hart's securities exchange model, Journal of Economic Theory 41, 392-404 (1987).  Page, F.H.Jr., Wooders, M.H., A necessary and su�cient condition for compactness of individually rational and feasible outcomes and the existence of an equilibrium, Economics Letters 52, 153-162 (1996).  Page, F.H.Jr., Wooders, M.H., Monteiro, P.K., Inconsequential arbitrage, Journal of Mathematical Economics 34, 439-469 (2000).  Rockafellar, R.T., Convex Analysis, Princeton University Press, (1970).  Werner J., Arbitrage and the existence of competitive equilibrium, Econometrica 55, 1403-1418 (1987).|
Actions (login required)