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No-arbitrage and Equilibrium in Finite Dimension: A General Result

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Abstract

We consider an exchange economy with a finite number of assets and a finite number of agents. The utility functions of the agents are concave, strictly increasing and their suprema equal infity. We use weak no-arbitrage prices a la Dana and Le Van [5]. Our main result is: an equilibrium exists if, and only if, their exists a weak no-arbitrage price common to all the agents

Suggested Citation

  • 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.
    • Handle: RePEc:mse:cesdoc:17023
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    1. Donald J. Brown & Jan Werner, 1995. "Arbitrage and Existence of Equilibrium in Infinite Asset Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(1), pages 101-114.
    2. Rose-Anne Dana & Cuong Le Van, 2010. "Overlapping sets of priors and the existence of efficient allocations and equilibria for risk measures," PSE-Ecole d'économie de Paris (Postprint) halshs-00308530, HAL.
    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. PageJr., Frank H. & Wooders, Myrna H. & Monteiro, Paulo K., 2000. "Inconsequential arbitrage," Journal of Mathematical Economics, Elsevier, vol. 34(4), pages 439-469, December.
    6. Geistdoerfer-Florenzano, Monique, 1982. "The gale-nikaido-debreu lemma and the existence of transitive equilibrium with or without the free-disposal assumption," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 113-134, January.
    7. Dana, R.A. & Le Van, C., 2010. "Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2186-2202, November.
    8. Ha-Huy, Thai & Le Van, Cuong, 2017. "Existence of equilibrium on asset markets with a countably infinite number of states," Journal of Mathematical Economics, Elsevier, vol. 73(C), pages 44-53.
    9. Page, Frank Jr., 1996. "Arbitrage and asset prices," Mathematical Social Sciences, Elsevier, vol. 31(3), pages 183-208, June.
    10. 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.
    11. Page, Frank Jr., 1987. "On equilibrium in Hart's securities exchange model," Journal of Economic Theory, Elsevier, vol. 41(2), pages 392-404, April.
    12. Frank H. Page Jr. & (**), Myrna H. Wooders & Paulo K. Monteiro, 1999. "Arbitrage and global cones: Another counterexample," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(2), pages 337-346.
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    14. Rose-Anne Dana & Cuong Le Van, 2010. "Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling," PSE-Ecole d'économie de Paris (Postprint) halshs-00470670, HAL.
    15. Rose-Anne Dana & Cuong Le Van, 2007. "Overlapping sets of priors and the existence of efficient allocations and equilibria for risk measures," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00188761, HAL.
    16. 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.
    17. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-1418, November.
    18. Grandmont, Jean-Michel, 1972. "Continuity properties of a von Neumann-Morgenstern utility," Journal of Economic Theory, Elsevier, vol. 4(1), pages 45-57, February.
    19. Rose-Anne Dana & Cuong Le Van, 2010. "Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling," Post-Print halshs-00470670, HAL.
    20. Grandmont, Jean-Michel, 1993. "Temporary general equilibrium theory," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 19, pages 879-922, Elsevier.
    21. Green, Jerry R, 1973. "Temporary General Equilibrium in a Sequential Trading Model with Spot and Futures Transactions," Econometrica, Econometric Society, vol. 41(6), pages 1103-1123, November.
    22. Rose-Anne Dana & Cuong Le Van, 2010. "Overlapping sets of priors and the existence of efficient allocations and equilibria for risk measures," Post-Print halshs-00308530, HAL.
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    24. Monteiro, Paulo K. & Page, Frank Jr. & Wooders, Myrna Holtz, 1997. "Arbitrage, equilibrium, and gains from trade: A counterexample," Journal of Mathematical Economics, Elsevier, vol. 28(4), pages 481-501, November.
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    More about this item

    Keywords

    asset market equilibrium; individually rational attainable allocations; individually rational utility set; no-arbitrage prices; weak no-arbitrage prices; no-arbitrage condition;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • G1 - Financial Economics - - General Financial Markets

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