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Linear and non-linear price decentralization

Author

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  • Charalambos Aliprantis

    () (Department of Economics - Purdue University [West Lafayette])

  • Monique Florenzano

    () (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Rabee Tourky

    () (Department of Economics - Purdue University [West Lafayette])

Abstract

Compendious and thorough solutions to the existence of a linear price equilibrium problem, the second welfare theorem, and the limit theorem on the core are provided for exchange economies whose consomption sets are the positive cone of arbitrary ordered Fréchet-dispensing entirely with the assumption that the vector ordering of the commodity space is a lattice. The motivation comes from economic applications showing the need to bring within the scope of equilibrium theory vector orderings that are not lattices, which arise in the typical model of portfolio trading with missing options. The assumptions are on the primitives of the model. They are bounds on the marginals of non-linear prives and for omega-proper economies they are both sufficient and necessary.

Suggested Citation

  • Charalambos Aliprantis & Monique Florenzano & Rabee Tourky, 2005. "Linear and non-linear price decentralization," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00086101, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00086101 DOI: 10.1016/j.jet.2004.04.007 Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00086101
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    References listed on IDEAS

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    1. Aliprantis, Charalambos D. & Monteiro, Paulo K. & Tourky, Rabee, 2004. "Non-marketed options, non-existence of equilibria, and non-linear prices," Journal of Economic Theory, Elsevier, vol. 114(2), pages 345-357, February.
    2. Aliprantis, Charalambos D & Brown, Donald J & Burkinshaw, Owen, 1987. "Edgeworth Equilibria," Econometrica, Econometric Society, vol. 55(5), pages 1109-1137, September.
    3. 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.
    4. Aliprantis, Charalambos D. & Tourky, Rabee, 2002. "Markets that don't replicate any option," Economics Letters, Elsevier, vol. 76(3), pages 443-447, August.
    5. Mas-Colell, Andreu & Richard, Scott F., 1991. "A new approach to the existence of equilibria in vector lattices," Journal of Economic Theory, Elsevier, vol. 53(1), pages 1-11, February.
    6. Stephen Clark, 2004. "A tangent cone analysis of smooth preferences on a topological vector space," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(2), pages 337-352, January.
    7. Richard, Scott F., 1989. "A new approach to production equilibria in vector lattices," Journal of Mathematical Economics, Elsevier, vol. 18(1), pages 41-56, February.
    8. Podczeck, Konrad, 1996. "Equilibria in vector lattices without ordered preferences or uniform properness," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 465-485.
    9. Rabee Tourky, 1999. "The limit theorem on the core of a production economy in vector lattices with unordered preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(1), pages 219-226.
    10. Nizar Allouch & Monique Florenzano, 2004. "Edgeworth and Walras equilibria of an arbitrage-free exchange economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(2), pages 353-370, January.
    11. Tourky, Rabee, 1998. "A New Approach to the Limit Theorem on the Core of an Economy in Vector Lattices," Journal of Economic Theory, Elsevier, vol. 78(2), pages 321-328, February.
    12. Valeri M. Marakulin, 2001. "Equilibria in infinite dimensional commodity spaces revisited," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(3), pages 621-633.
    13. Stephen A. Ross, 1976. "Options and Efficiency," The Quarterly Journal of Economics, Oxford University Press, vol. 90(1), pages 75-89.
    14. Aliprantis, Charalombos & Burkinshaw, Owen, 1991. "When Is the Core Equivalence Theorem Valid?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 169-182, April.
    15. Back, Kerry, 1988. "Structure of consumption sets and existence of equilibria in infinite-dimensional spaces," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 89-99, February.
    16. Aliprantis, Charalambos D. & Brown, Donald J. & Burkinshaw, Owen, 1987. "Edgeworth equilibria in production economies," Journal of Economic Theory, Elsevier, vol. 43(2), pages 252-291, December.
    17. Messaoud Deghdak & Monique Florenzano, 1999. "Decentralizing Edgeworth equilibria in economies with many commodities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(2), pages 297-310.
    18. Zame, William R, 1987. "Competitive Equilibria in Production Economies with an Infinite-Dimensional Commodity Space," Econometrica, Econometric Society, vol. 55(5), pages 1075-1108, September.
    19. 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.
    20. Araujo, A. & Monteiro, P. K., 1989. "Equilibrium without uniform conditions," Journal of Economic Theory, Elsevier, vol. 48(2), pages 416-427, August.
    21. 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.
    22. Donald A. Walker (ed.), 2000. "Equilibrium," Books, Edward Elgar Publishing, volume 0, number 1585, April.
    23. Robert A. Jarrow & Xing Jin & Dilip B. Madan, 1999. "The Second Fundamental Theorem of Asset Pricing," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 255-273.
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    Citations

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    Cited by:

    1. Carlos Hervés-Beloso & V. Martins-da-Rocha & Paulo Monteiro, 2009. "Equilibrium theory with asymmetric information and infinitely many states," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 295-320, February.
    2. Martins-da-Rocha, V. Filipe & Riedel, Frank, 2010. "On equilibrium prices in continuous time," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1086-1112, May.
    3. Achille Basile & Maria Gabriella Graziano, 2012. "Core Equivalences for Equilibria Supported by Non-linear Prices," CSEF Working Papers 309, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    4. Roko Aliprantis & Monique Florenzano & Daniella Puzzello & Rabee Tourky, 2006. "The wedge of arbitrage free prices : anything goes," Cahiers de la Maison des Sciences Economiques b06070, Université Panthéon-Sorbonne (Paris 1).
    5. Charalambos D. Aliprantis & Monique Florenzano & Rabee Tourky, 2004. "Equilibria in production economies," Cahiers de la Maison des Sciences Economiques b04116, Université Panthéon-Sorbonne (Paris 1).
    6. V. Martins-da-Rocha & Frank Riedel, 2006. "Stochastic equilibria for economies under uncertainty with intertemporal substitution," Annals of Finance, Springer, vol. 2(1), pages 101-122, January.
    7. Aliprantis, Charalambos D. & Florenzano, Monique & Tourky, Rabee, 2006. "Production equilibria," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 406-421, August.
    8. Klishchuk, Bogdan, 2015. "New conditions for the existence of Radner equilibrium with infinitely many states," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 67-73.

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