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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)

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    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. Allouch, 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.

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    Bibliographic Info

    Paper provided by Development and Policies Research Center (DEPOCEN), Vietnam in its series Working Papers with number 04.

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    Length: 6 pages
    Date of creation: Jan 2008
    Date of revision:
    Handle: RePEc:dpc:wpaper:0408

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    Keywords: Arbitrage; Competitive equilibrium;

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    1. 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.
    2. Dana, R.-A. & Le Van, C. & Magnien, F., 1999. "On the Different Notions of Arbitrage and Existence of Equilibrium," Papiers d'Economie Mathématique et Applications, Université Panthéon-Sorbonne (Paris 1) 1999.34, Université Panthéon-Sorbonne (Paris 1).
    3. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 55(6), pages 1403-18, November.
    4. 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, Elsevier, vol. 52(2), pages 153-162, August.
    5. Hart, Oliver D., 1974. "On the existence of equilibrium in a securities model," Journal of Economic Theory, Elsevier, Elsevier, vol. 9(3), pages 293-311, November.
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