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No unbounded arbitrage, weak no market arbitrage and no arbitrage price system conditions: The circular results

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  • Manh-Hung Nguyen

    (THEMA, Cergy-Pontoise University)

  • Thai Ha-Huy

    (CES, Paris-1 Pantheon-Sorbonne University)

Abstract

Page and Wooders (1996) prove that the no-unbounded-arbitrage (NUBA) condition introduced by Page (1987) is equivalent to the existence of a no arbitrage price (NAPS) when no agent has non-null useless vectors. Al- louch, Le Van and Page (2002) show that their generalized NAPS condition is actually equivalent to the weak-no-market-arbitrage (WNMA) condition introduced by Hart (1974). They mention that this result implies the one given by Page andWooders (1996). In this note, we show that these results are actually circular.

Suggested Citation

  • Manh-Hung Nguyen & Thai Ha-Huy, 2008. "No unbounded arbitrage, weak no market arbitrage and no arbitrage price system conditions: The circular results," THEMA Working Papers 2008-08, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    • Handle: RePEc:ema:worpap:2008-08
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    References listed on IDEAS

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    1. 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.
    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. 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.
    4. Page, Frank Jr., 1987. "On equilibrium in Hart's securities exchange model," Journal of Economic Theory, Elsevier, vol. 41(2), pages 392-404, April.
    5. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-1418, November.
    6. 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.
    7. repec:dau:papers:123456789/6228 is not listed on IDEAS
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    More about this item

    Keywords

    Arbitrage; Equilibrium; Recession cone.;
    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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