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Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling

Author

Listed:
  • Rose-Anne Dana

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Cuong Le Van

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, University of Exeter Business School - University of Exeter, 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)

Abstract
The theory of existence of equilibrium with short-selling is reconsidered under risk and ambiguity modelled by risk averse variational preferences. A sufficient condition for existence of efficient allocations is that the relative interiors of the risk adjusted sets of expectations overlap. This condition is necessary if agents are not risk neutral at extreme levels of wealths either positive or negative. It is equivalent to the condition that there does not exist mutually compatible trades, with non negative expected value with respect to any risk adjusted prior, strictly positive for some agent and some prior. It is shown that the more uncertainty averse and the more risk averse the agents, the more likely are efficient allocations and equilibria to exist.

Suggested Citation

  • Rose-Anne Dana & Cuong Le Van, 2010. "Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00470670, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00470670
    DOI: 10.1016/j.jet.2010.08.002
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00470670
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    More about this item

    Keywords

    Uncertainty; risk; common prior; equilibria with shortselling; Variational preferences;
    All these keywords.

    JEL classification:

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

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