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Inconsequential arbitrage

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  • PageJr., Frank H.
  • Wooders, Myrna H.
  • Monteiro, Paulo K.

Abstract

We introduce the concept of inconsequential arbitrage and, in the context of a model allowing short-sales and half-lines in indifference surfaces, we prove that inconsequential arbitrage is sufficient for existence of equilibrium. With a slightly stronger condition of local nonsatiation than required for existence of equilibrium and with a mild uniformity condition on arbitrage opportunities, we show that the existence of a pareto-optimal allocation implies inconsequential arbitrage, implying that inconsequential arbitrage is necessary and sufficient for existence of an equilibrium.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 34 (2000)
Issue (Month): 4 (December)
Pages: 439-469

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Handle: RePEc:eee:mateco:v:34:y:2000:i:4:p:439-469

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  1. 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).
  2. 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.
  3. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March.
  4. Brown,Donald & Werner,Jan, 1991. "Arbitrage and existence of equilibrium in infinite asset markets," Discussion Paper Serie A 344, University of Bonn, Germany.
  5. Nielsen, Lars Tyge, 1989. "Asset Market Equilibrium with Short-Selling," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 56(3), pages 467-73, July.
  6. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 55(6), pages 1403-18, November.
  7. 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.
  8. Hammond, Peter J., 1983. "Overlapping expectations and Hart's conditions for equilibrium in a securities model," Journal of Economic Theory, Elsevier, vol. 31(1), pages 170-175, October.
  9. Chichilnisky, Graciela, 1997. "A topological invariant for competitive markets," Journal of Mathematical Economics, Elsevier, vol. 28(4), pages 445-469, November.
  10. Grandmont, Jean-Michel, 1977. "Temporary General Equilibrium Theory," Econometrica, Econometric Society, Econometric Society, vol. 45(3), pages 535-72, April.
  11. Frank H. Page Jr. & (**), Myrna H. Wooders & Paulo K. Monteiro, 1999. "Arbitrage and global cones: Another counterexample," Social Choice and Welfare, Springer, Springer, vol. 16(2), pages 337-346.
  12. Reny, Philip J. & Holtz Wooders, Myrna, 1996. "The Partnered Core of a Game without Side Payments," Journal of Economic Theory, Elsevier, vol. 70(2), pages 298-311, August.
  13. Green, Jerry R, 1973. "Temporary General Equilibrium in a Sequential Trading Model with Spot and Futures Transactions," Econometrica, Econometric Society, Econometric Society, vol. 41(6), pages 1103-23, November.
  14. Page Jr., Frank H. & Wooders, Myrna Holtz, 1996. "The Partnered Core of an Economy and the Partnered Competitive Equilibrium," Economics Letters, Elsevier, vol. 52(2), pages 143-152, August.
  15. Bergstrom, Theodore C., 1976. "How to discard `free disposability' - at no cost," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 131-134, July.
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