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Arbitrage and asset market equilibrium in infinite dimensional economies with short-selling and risk-averse expected utilities

Author

Listed:
  • Thai Ha-Huy

    () (EPEE - Centre d'Etudes des Politiques Economiques - UEVE - Université d'Évry-Val-d'Essonne)

  • Cuong Le Van

    () (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne, IPAG Business School, VCREME - Van Xuan Center of Research in Economics, Management and Environment, PSE - Paris School of Economics)

  • Nguyen Manh Hung

    () (TSE - Toulouse School of Economics - UT1 - Université Toulouse 1 Capitole - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

Abstract

We consider a model with an infinite number of states of nature, von Neumann - Morgenstern utilities, where agents have different probability beliefs and where short sells are allowed. We show that no-arbitrage conditions, defined for finite dimensional asset markets models, are not sufficient to ensure existence of equilibrium in presence of an infinite number of states of nature. However, if the individually rational utility set U is compact, we obtain an equilibrium. We give conditions which imply the compactness of U. We give examples of non-existence of equilibrium when these conditions do not hold.

Suggested Citation

  • Thai Ha-Huy & Cuong Le Van & Nguyen Manh Hung, 2016. "Arbitrage and asset market equilibrium in infinite dimensional economies with short-selling and risk-averse expected utilities," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01390954, HAL.
  • Handle: RePEc:hal:cesptp:halshs-01390954
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01390954
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    References listed on IDEAS

    as
    1. Donald J. Brown & Jan Werner, 1995. "Arbitrage and Existence of Equilibrium in Infinite Asset Markets," Review of Economic Studies, Oxford University Press, vol. 62(1), pages 101-114.
    2. Dana, R. A. & Le Van, C., 1996. "Asset Equilibria in Lp spaces with complete markets: A duality approach," Journal of Mathematical Economics, Elsevier, vol. 25(3), pages 263-280.
    3. Wassim Daher & V. Martins-da-Rocha & Yiannis Vailakis, 2007. "Asset market equilibrium with short-selling and differential information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(3), pages 425-446, September.
    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. 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.
    6. PageJr., Frank H. & Wooders, Myrna H. & Monteiro, Paulo K., 2000. "Inconsequential arbitrage," Journal of Mathematical Economics, Elsevier, vol. 34(4), pages 439-469, December.
    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. 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.
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    11. Won, Dong Chul & Yannelis, Nicholas C., 2008. "Equilibrium theory with unbounded consumption sets and non-ordered preferences: Part I. Non-satiation," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1266-1283, December.
    12. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-1418, November.
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    Cited by:

    1. 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.

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