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The geometry of arbitrage and the existence of competitive equilibrium

Author

Listed:
  • Allouch, Nizar
  • Le Van, Cuong
  • Page, Jr. Frank H.
Abstract
We present the basic geometry of arbitrage and use this basic geometry to shed new light on the relationships between various noarbitrage conditions found in the literature. For example, under very mild conditions of Hart (1974) and Werner (1987) are equivalent and imply the compactness of the set of utility possibilities. Moreover, we show that if agents' sets of useless net trades are linearly independent, then the Hart-Werner conditions are equilivent to the stronger condition of no-unbounded-arbitrage due to Page (1987) - and, in turn, all are equilivalent to compactness of the set of rational allocations. We also consider the problem of existence of equilibrium. We show, for example, that under a uniformity condition on preferences weaker than Werner's uniformity condition, the Hart-Werner no-arbitrage conditions are sufficient for existence. With an additional condition of weak no half lines - a condition weaker than Werner's no-half lines condition - we show that the Hart-Werner conditions are both necessary and sufficient for existence.

Suggested Citation

  • Allouch, Nizar & Le Van, Cuong & Page, Jr. Frank H., 2001. "The geometry of arbitrage and the existence of competitive equilibrium," The Warwick Economics Research Paper Series (TWERPS) 598, University of Warwick, Department of Economics.
    • Handle: RePEc:wrk:warwec:598
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    References listed on IDEAS

    as
    1. Donald J. Brown & Jan Werner, 1995. "Arbitrage and Existence of Equilibrium in Infinite Asset Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(1), pages 101-114.
    2. Milne, Frank, 1980. "Short-Selling, Default Risk and the Existence of Equilibrium in a Securities Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(2), pages 255-267, June.
    3. Allouch, Nizar, 2002. "An equilibrium existence result with short selling," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 81-94, April.
    4. Dana, Rose-Anne & Le Van, Cuong & Magnien, Francois, 1999. "On the Different Notions of Arbitrage and Existence of Equilibrium," Journal of Economic Theory, Elsevier, vol. 87(1), pages 169-193, July.
    5. PageJr., Frank H. & Wooders, Myrna H. & Monteiro, Paulo K., 2000. "Inconsequential arbitrage," Journal of Mathematical Economics, Elsevier, vol. 34(4), pages 439-469, December.
    6. Allouch, Nizar & Van, Cuong Le & Page Jr. Frank H., 2002. "Arbitrage, Equilibrium And Nonsatiation," The Warwick Economics Research Paper Series (TWERPS) 637, University of Warwick, Department of Economics.
    7. Allouch, N., 2000. "Equilibrium and Bounded Arbitrage," Papiers d'Economie Mathématique et Applications 2000.78, Université Panthéon-Sorbonne (Paris 1).
    8. Lars Tyge Nielsen, 1989. "Asset Market Equilibrium with Short-Selling," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(3), pages 467-473.
    9. Page Jr., Frank H. & Wooders, Myrna Holtz, 1996. "A necessary and sufficient condition for the compactness of individually rational and feasible outcomes and the existence of an equilibrium," Economics Letters, Elsevier, vol. 52(2), pages 153-162, August.
    10. Page, Frank Jr., 1987. "On equilibrium in Hart's securities exchange model," Journal of Economic Theory, Elsevier, vol. 41(2), pages 392-404, April.
    11. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-1418, November.
    12. Grandmont, Jean-Michel, 1972. "Continuity properties of a von Neumann-Morgenstern utility," Journal of Economic Theory, Elsevier, vol. 4(1), pages 45-57, February.
    13. Hart, Oliver D., 1974. "On the existence of equilibrium in a securities model," Journal of Economic Theory, Elsevier, vol. 9(3), pages 293-311, November.
    14. 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.
    15. Milne, Frank, 1976. "Default Risk in a General Equilibrium Asset Economy with Incomplete Markets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(3), pages 613-625, October.
    16. Green, Jerry R, 1973. "Temporary General Equilibrium in a Sequential Trading Model with Spot and Futures Transactions," Econometrica, Econometric Society, vol. 41(6), pages 1103-1123, November.
    17. Chongmin Kim, 1998. "Stochastic Dominance, Pareto Optimality, and Equilibrium Asset Pricing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(2), pages 341-356.
    18. repec:dau:papers:123456789/6228 is not listed on IDEAS
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    More about this item

    Keywords

    ARBITRAGE ; COMPETITIVE EQUILIBRIUM ; RECESSION CONES;
    All these keywords.

    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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