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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 - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, IPAG Business School, VCREME - Van Xuan Center of Research in Economics, Management and Environment, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Nguyen Manh Hung

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - 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://shs.hal.science/halshs-01390954
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    References listed on IDEAS

    as
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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.
    2. Thai Ha-Huy & Cuong Le Van, 2012. "Asset market equilibrium with short-selling and a continuum of number of states of nature," Working Papers hal-04132780, HAL.

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    More about this item

    Keywords

    asset market equilibrium; individually rational attainable allocations; individually rational utility set; 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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