No unbounded arbitrage, weak no market arbitrage and no arbitrage price system conditions: The circular results
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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- 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.
- 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.
- 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.
- Dana, R.-A. & Le Van, C. & Magnien, F., 1999. "On the Different Notions of Arbitrage and Existence of Equilibrium," Papiers d'Economie MathÃ©matique et Applications 1999.34, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
- Page, Frank Jr., 1987. "On equilibrium in Hart's securities exchange model," Journal of Economic Theory, Elsevier, vol. 41(2), pages 392-404, April.
- Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-1418, November.
- 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.
- 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.
- 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.
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