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No unbounded arbitrage, weak no market arbitrage and no arbitrage price system conditions; Equivalent conditions

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  • Nguyen, Manh-Hung
  • Ha-Huy, Thai

Abstract

Page and Wooders [Page Jr., F.H., Wooders, M., 1996. A necessary and sufficient condition for compactness of individually rational and feasible outcomes and existence of an equilibrium. Economics Letters 52, 153-162] prove that the no unbounded arbitrage (NUBA), a special case of a condition in Page [Page, F.H., 1987. On equilibrium in Hart's securities exchange model. Journal of Economic Theory 41, 392-404], is equivalent to the existence of a no arbitrage price system (NAPS) when no agent has non-null useless vectors. Allouch et al. [Allouch, N., Le Van, C., Page F.H., 2002. The geometry of arbitrage and the existence of competitive equilibrium. Journal of Mathematical Economics 38, 373-391] extend the NAPS introduced by Werner [Werner, J., 1987. Arbitrage and the existence of competitive equilibrium. Econometrica 55, 1403-1418] and show that this condition is equivalent to the weak no market arbitrage (WNMA) of Hart [Hart, O., 1974. On the existence of an equilibrium in a securities model. Journal of Economic Theory 9, 293-311]. They mention that this result implies the one given by Page and Wooders [Page Jr., F.H., Wooders, M., 1996. A necessary and sufficient condition for compactness of individually rational and feasible outcomes and existence of an equilibrium. Economics Letters 52, 153-162]. In this note, we show that all these conditions are equivalent.

Suggested Citation

  • Nguyen, Manh-Hung & Ha-Huy, Thai, 2010. "No unbounded arbitrage, weak no market arbitrage and no arbitrage price system conditions; Equivalent conditions," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 128-131, January.
    • Handle: RePEc:eee:mateco:v:46:y:2010:i:1:p:128-131
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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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    Cited by:

    1. Thai Ha-Huy & Cuong Le Van & Frank Page & Myrna Wooders, 2017. "No-arbitrage and Equilibrium in Finite Dimension: A General Result," Documents de travail du Centre d'Economie de la Sorbonne 17023, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. Sato Norihisa, 2010. "Existence of Competitive Equilibrium in Unbounded Exchange Economies with Satiation: A Note," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-22, July.

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