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

  • Manh-Hung Nguyen

    ()

    (THEMA, Cergy-Pontoise University)

  • Thai Ha-Huy

    ()

    (CES, Paris-1 Pantheon-Sorbonne University)

Registered author(s):

    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.

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    Paper provided by THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise in its series THEMA Working Papers with number 2008-08.

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    Date of creation: 2008
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    Handle: RePEc:ema:worpap:2008-08
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    1. Dana, Rose-Anne & Le Van, Cuong & Magnien, François, 1996. "On the different notions of arbitrage and existence of equilibrium," CEPREMAP Working Papers (Couverture Orange) 9616, CEPREMAP.
    2. 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.
    3. 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.
    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, vol. 52(2), pages 153-162, August.
    5. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-18, November.
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