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Arbitrage, Equilibrium, and Nonsatiation

Author

Listed:
  • Nizar Allouch

    (Queen Mary, University of London)

  • Cuong Le Van

    () (University of Paris 1)

  • Frank H. Page, Jr.

    () (University of Alabama)

Abstract

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 unbounded 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.

Suggested Citation

  • Nizar Allouch & Cuong Le Van & Frank H. Page, Jr., 2004. "Arbitrage, Equilibrium, and Nonsatiation," Working Papers 512, Queen Mary University of London, School of Economics and Finance.
  • Handle: RePEc:qmw:qmwecw:wp512
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    File URL: http://www.econ.qmul.ac.uk/media/econ/research/workingpapers/archive/wp512.pdf
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    References listed on IDEAS

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    1. 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.
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    3. Grandmont, Jean-Michel, 1993. "Temporary general equilibrium theory," Handbook of Mathematical Economics,in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 19, pages 879-922 Elsevier.
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    8. Dana, Rose-Anne & Le Van, Cuong & Magnien, Francois, 1999. "On the Different Notions of Arbitrage and Existence of Equilibrium," Journal of Economic Theory, Elsevier, pages 169-193.
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    Cited by:

    1. 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), pages 353-370.
    2. Allouch, Nizar & Le Van, Cuong & Page, Frank Jr., 2002. "The geometry of arbitrage and the existence of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 38(4), pages 373-391, December.
    3. repec:hal:journl:halshs-00086096 is not listed on IDEAS

    More about this item

    Keywords

    Arbitrage; Asset market equilibrium; Nonsatiation; Recession cones;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

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