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Equilibria in Incomplete Assets Economies with Infinite Dimensional Spot Markets

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  • Aliprantis, C. D.
  • Tourky, Rabee
Abstract
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 quasi-interior 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.

Suggested Citation

  • Aliprantis, C. D. & Tourky, Rabee, 2004. "Equilibria in Incomplete Assets Economies with Infinite Dimensional Spot Markets," Purdue University Economics Working Papers 1169, Purdue University, Department of Economics.
    • Handle: RePEc:pur:prukra:1169
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    References listed on IDEAS

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    1. Levine, David K., 1989. "Infinite horizon equilibrium with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 18(4), pages 357-376, September.
    2. Magill, Michael & Quinzii, Martine, 1994. "Infinite Horizon Incomplete Markets," Econometrica, Econometric Society, vol. 62(4), pages 853-880, July.
    3. 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 189-207, April.
    4. Mas-Colell, Andreu & Monteiro, Paulo K., 1996. "Self-fulfilling equilibria: An existence theorem for a general state space," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 51-62.
    5. Magill, Michael & Quinzii, Martine, 1996. "Incomplete markets over an infinite horizon: Long-lived securities and speculative bubbles," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 133-170.
    6. 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 103-131.
    7. Mas-Colell, Andreu, 1975. "A model of equilibrium with differentiated commodities," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 263-295.
    8. Husseini, S. Y. & Lasry, J. -M. & Magill, M. J. P., 1990. "Existence of equilibrium with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 39-67.
    9. Jones, Larry E., 1987. "Existence of equilibria with infinitely many commodities : Banach lattices reconsidered," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 89-104, April.
    10. Busch, Lutz-Alexander & Govindan, Srihari, 2004. "Robust nonexistence of equilibrium with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 641-645, September.
    11. 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 1523-1614, Elsevier.
    12. Aliprantis, Charalambos D & Brown, Donald J & Burkinshaw, Owen, 1987. "Edgeworth Equilibria," Econometrica, Econometric Society, vol. 55(5), pages 1109-1137, September.
    13. 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 85-101.
    14. Werner, Jan, 1989. "Equilibrium with incomplete markets without ordered preferences," Journal of Economic Theory, Elsevier, vol. 49(2), pages 379-382, December.
    15. Hart, Oliver D., 1975. "On the optimality of equilibrium when the market structure is incomplete," Journal of Economic Theory, Elsevier, vol. 11(3), pages 418-443, December.
    16. Mas-Colell, Andreu, 1986. "The Price Equilibrium Existence Problem in Topological Vector Lattice s," Econometrica, Econometric Society, vol. 54(5), pages 1039-1053, September.
    17. Werner, Jan, 1985. "Equilibrium in economies with incomplete financial markets," Journal of Economic Theory, Elsevier, vol. 36(1), pages 110-119, June.
    18. Mas-Colell, Andreu & Zame, William R., 1996. "The existence of security market equilibrium with a non-atomic state space," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 63-84.
    19. Geanakoplos, John, 1990. "An introduction to general equilibrium with incomplete asset markets," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 1-38.
    20. Yannelis, Nicholas C. & Zame, William R., 1986. "Equilibria in Banach lattices without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 15(2), pages 85-110, April.
    21. Duffie, Darrell & Shafer, Wayne, 1985. "Equilibrium in incomplete markets: I : A basic model of generic existence," Journal of Mathematical Economics, Elsevier, vol. 14(3), pages 285-300, June.
    22. 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 207-219, December.
    23. Araujo, A. & Monteiro, P. K., 1989. "Equilibrium without uniform conditions," Journal of Economic Theory, Elsevier, vol. 48(2), pages 416-427, August.
    24. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
    25. Donald A. Walker (ed.), 2000. "Equilibrium," Books, Edward Elgar Publishing, volume 0, number 1585.
    26. BEWLEY, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," LIDAM Reprints CORE 122, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    27. 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 233-245, December.
    28. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March.
    29. Duffie, Darrell, 1996. "Incomplete security markets with infinitely many states: An introduction," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 1-8.
    30. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
    31. 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 347-366, October.
    32. Toussaint, Sabine, 1984. "On the existence of equilibria in economies with infinitely many commodities and without ordered preferences," Journal of Economic Theory, Elsevier, vol. 33(1), pages 98-115, June.
    33. 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 455-461, March.
    34. 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 165-169, October.
    35. W. Hildenbrand & H. Sonnenschein (ed.), 1991. "Handbook of Mathematical Economics," Handbook of Mathematical Economics, Elsevier, edition 1, volume 4, number 4.
    36. Mas-Colell, 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 1835-1898, Elsevier.
    37. Hernandez D., Alejandro & Santos, Manuel S., 1996. "Competitive Equilibria for Infinite-Horizon Economies with Incomplete Markets," Journal of Economic Theory, Elsevier, vol. 71(1), pages 102-130, October.
    38. Aliprantis, Charalambos D. & Tourky, Rabee & Yannelis, Nicholas C., 2000. "Cone Conditions in General Equilibrium Theory," Journal of Economic Theory, Elsevier, vol. 92(1), pages 96-121, May.
    39. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, January.
    40. Hellwig, Martin, 1996. "Rational expectations equilibria in sequence economies with symmetric information: The two-period case," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 9-49.
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    2. Foivos Xanthos, 2014. "Non-existence of weakly Pareto optimal allocations," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(2), pages 137-146, October.

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    More about this item

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • D60 - Microeconomics - - Welfare Economics - - - General

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