Equilibria in Incomplete Assets Economies with Infinite Dimensional Spot Markets
The paper studies the two period incomplete markets model where assets are claims on state contingent commodity bundles and there are no bounds on portfolio trading. The important results on the existence of equilibrium in this model assume that there is a finite number of commodities traded in each spot market and that preferences are given by smooth utility functions. With these assumptions an equilibrium exists outside an “exceptional” set of assets structures and initial endowments. The present paper extends these results by allowing for general infinite dimensional commodity spaces in each spot market. These include all the important commodity spaces studied in the literature on the existence of Walrasian equilibrium – in each spot market the consumption sets are the positive cone of an arbitrary locally solid Riesz space or of an ordered topological vector space with order unit or of a locally solid Riesz space with quasiinterior point. The paper establishes that even with our very general commodity spaces there exists an equilibrium for a “very” dense set of assets structures. Our approach is in the main convex analytic and the results do not require that preferences be smooth or complete or transitive. The typical situation in infinite dimensional commodity spaces does not readily allow for the kind of differential analysis and smoothness assumptions used in the finite dimensional setting. In the general settings that we study it seems that one is restricted to convex analytic techniques and assumptions. Therefore, the concepts and techniques studied in this paper also have important finite dimensional applications.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Length:  37 pages 
Date of creation:  Sep 2004 
Date of revision:  
Handle:  RePEc:pur:prukra:1169 
Contact details of provider:  Postal: Web page: http://www.krannert.purdue.edu/programs/phd More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
 Magill, M. & Quinzii, M., 1992.
"Infinite Horizon Incomplete Markets,"
Papers
413a, California Davis  Institute of Governmental Affairs.
 Magill, Michael & Quinzii, Martine, 1994. "Infinite Horizon Incomplete Markets," Econometrica, Econometric Society, vol. 62(4), pages 85380, July.
 Magill, M. & Quinzii, M., 1993. "Infinite Horizon Incomplete Markets," Papers 9320, Southern California  Department of Economics.
 Magill, M. & Quinzii, M., 1992. "Infinite Horizon Incomplete Markets," DELTA Working Papers 9226, DELTA (Ecole normale supérieure).
 Magill,Michael & Quinzii,Martine, 1992. "Infinite horizon,Incomplete markets," Discussion Paper Serie A 384, University of Bonn, Germany.
 David K. Levine & William Zame, 1996.
"Debt Constraints and Equilibrium in Infinite Horizon Economies with Incomplete Markets,"
Levine's Working Paper Archive
1954, David K. Levine.
 Levine, David K. & Zame, William R., 1996. "Debt constraints and equilibrium in infinite horizon economies with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 103131.
 David K. Levine & William R. Zame, 1993. "Debt Constraints and Equilibrium in Infinite Horizon Economies with Incomplete Markets," UCLA Economics Working Papers 703, UCLA Department of Economics.
 David K. Levine & William R. Zame, 1992. "Debt Constraints and Equilibrium in Infinite Horizon Economies with Incomplete Markets," UCLA Economics Working Papers 666, UCLA Department of Economics.
 Hellwig, Martin, 1996. "Rational expectations equilibria in sequence economies with symmetric information: The twoperiod case," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 949.
 Geanakoplos, John, 1990. "An introduction to general equilibrium with incomplete asset markets," Journal of Mathematical Economics, Elsevier, vol. 19(12), pages 138.
 Levine, David K., 1989.
"Infinite horizon equilibrium with incomplete markets,"
Journal of Mathematical Economics,
Elsevier, vol. 18(4), pages 357376, September.
 David K. Levine, 1989. "Infinite Horizon Equilibrium with Incomplete Markets," Levine's Working Paper Archive 49, David K. Levine.
 Magill, M. & Quinzii, M., 1993.
"Icomplete Markets Over an Infinite Horizon: LongLived Securities and Speculative Bubbles,"
Papers
9321, Southern California  Department of Economics.
 Magill, Michael & Quinzii, Martine, 1996. "Incomplete markets over an infinite horizon: Longlived securities and speculative bubbles," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 133170.
 Araujo, Aloisio, 1985. "Lack of Pareto Optimal Allocations in Economies with Infinitely Many Commodities: The Need for Impatience," Econometrica, Econometric Society, vol. 53(2), pages 45561, March.
 Hart, Oliver D., 1975. "On the optimality of equilibrium when the market structure is incomplete," Journal of Economic Theory, Elsevier, vol. 11(3), pages 418443, December.
 Shafer, Wayne & Sonnenschein, Hugo, 1975.
"Equilibrium in abstract economies without ordered preferences,"
Journal of Mathematical Economics,
Elsevier, vol. 2(3), pages 345348, December.
 Wayne Shafer & Hugo Sonnenschein, 1974. "Equilibrium in Abstract Economies Without Ordered Preferences," Discussion Papers 94, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
 Aliprantis, Charalambos D. & Brown, Donald J., 1983.
"Equilibria in markets with a Riesz space of commodities,"
Journal of Mathematical Economics,
Elsevier, vol. 11(2), pages 189207, April.
 Aliprantis, Charalambos D. & Brown, D. J., 1982. "Equilibrium in Markets with a Riesz Space of Commodities," Working Papers 427, California Institute of Technology, Division of the Humanities and Social Sciences.
 Aliprantis, Charalambos D & Brown, Donald J & Burkinshaw, Owen, 1987.
"Edgeworth Equilibria,"
Econometrica,
Econometric Society, vol. 55(5), pages 110937, September.
 Donald J. Brown & Charalambos Aliprantis & Owen Burkinshaw, 1985. "Edgeworth Equilibria," Cowles Foundation Discussion Papers 756R, Cowles Foundation for Research in Economics, Yale University.
 Araujo, A. & Monteiro, P. K., 1989. "Equilibrium without uniform conditions," Journal of Economic Theory, Elsevier, vol. 48(2), pages 416427, August.
 Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514540, June.
 MasColell, Andreu, 1975. "A model of equilibrium with differentiated commodities," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 263295.
 Florenzano Monique, 1982.
"On the existence of equilibria in economies with an infinite dimensional commodity space,"
CEPREMAP Working Papers (Couverture Orange)
8217, CEPREMAP.
 Florenzano, Monique, 1983. "On the existence of equilibria in economies with an infinite dimensional commodity space," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 207219, December.
 MasColell, Andreu & Zame, William R., 1996. "The existence of security market equilibrium with a nonatomic state space," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 6384.
 Aliprantis, C. D. & Brown, D. J. & Polyrakis, I. A. & Werner, J., 1998.
"Portfolio dominance and optimality in infinite security markets,"
Journal of Mathematical Economics,
Elsevier, vol. 30(3), pages 347366, October.
 Aliprantis, C. D. & D. J. Brown & I. A. Polyrakis & J. Werner, 1996. "Portfolio Dominance and Optimality in Infinite Security Markets," Discussion Paper Serie B 383, University of Bonn, Germany.
 MasColell, Andreu & Zame, William R., 1991. "Equilibrium theory in infinite dimensional spaces," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 34, pages 18351898 Elsevier.
 Werner, Jan, 1985. "Equilibrium in economies with incomplete financial markets," Journal of Economic Theory, Elsevier, vol. 36(1), pages 110119, June.
 Monteiro, Paulo Klinger, 1996.
"A new proof of the existence of equilibrium in incomplete market economies,"
Journal of Mathematical Economics,
Elsevier, vol. 26(1), pages 85101.
 Paulo Klinger Monteiro, 1994. "A New Proof Of The Existence Of Equilibrium In Incomplete Markets Economies," GE, Growth, Math methods 9410001, EconWPA.
 Hernandez D., Alejandro & Santos, Manuel S., 1996. "Competitive Equilibria for InfiniteHorizon Economies with Incomplete Markets," Journal of Economic Theory, Elsevier, vol. 71(1), pages 102130, October.
 Gale, D. & MasColell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 915, March.
 Yannelis, Nicholas C. & Prabhakar, N. D., 1983. "Existence of maximal elements and equilibria in linear topological spaces," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 233245, December.
 Khan, M. Ali, 1984. "A remark on the existence of equilibria in markets without ordered preferences and with a Riesz space of commodities," Journal of Mathematical Economics, Elsevier, vol. 13(2), pages 165169, October.
 MasColell, Andreu & Monteiro, Paulo K., 1996. "Selffulfilling equilibria: An existence theorem for a general state space," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 5162.
 Aliprantis, Charalambos D. & Tourky, Rabee & Yannelis, Nicholas C., 2000. "Cone Conditions in General Equilibrium Theory," Journal of Economic Theory, Elsevier, vol. 92(1), pages 96121, May.
 Donald A. Walker (ed.), 2000. "Equilibrium," Books, Edward Elgar, volume 0, number 1585, 6.
 Magill, Michael & Shafer, Wayne, 1991. "Incomplete markets," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 30, pages 15231614 Elsevier.
 Busch, LutzAlexander & Govindan, Srihari, 2004. "Robust nonexistence of equilibrium with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 641645, September.
 Werner,Jan, 1988.
"Equilibrium with incomplete markets without ordered preferences,"
Discussion Paper Serie A
184, University of Bonn, Germany.
 Werner, Jan, 1989. "Equilibrium with incomplete markets without ordered preferences," Journal of Economic Theory, Elsevier, vol. 49(2), pages 379382, December.
 Husseini, S. Y. & Lasry, J. M. & Magill, M. J. P., 1990. "Existence of equilibrium with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 19(12), pages 3967.
 Yannelis, Nicholas C. & Zame, William R., 1986. "Equilibria in Banach lattices without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 15(2), pages 85110, April.
 Jones, Larry E., 1987. "Existence of equilibria with infinitely many commodities : Banach lattices reconsidered," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 89104, April.
This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.
When requesting a correction, please mention this item's handle: RePEc:pur:prukra:1169. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Krannert PHD)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.