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

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  • Ha-Huy, Thai
  • Le Van, Cuong
  • Nguyen, Manh-Hung

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

  • Ha-Huy, Thai & Le Van, Cuong & Nguyen, Manh-Hung, 2016. "Arbitrage and asset market equilibrium in infinite dimensional economies with short-selling and risk-averse expected utilities," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 30-39.
    • Handle: RePEc:eee:matsoc:v:79:y:2016:i:c:p:30-39
    DOI: 10.1016/j.mathsocsci.2015.10.007
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    Cited by:

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    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

    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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