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No-arbitrage, overlapping sets of priors and the existence of efficient allocations and equilibria in the presence of risk and ambiguity

Author

Listed:
  • Rose-Anne Dana

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

  • Cuong Le Van

    () (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics)

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 more likely are efficient allocations and equilibria to exist.

Suggested Citation

  • Rose-Anne Dana & Cuong Le Van, 2009. "No-arbitrage, overlapping sets of priors and the existence of efficient allocations and equilibria in the presence of risk and ambiguity," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00281582, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00281582 Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00281582v2
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    References listed on IDEAS

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    More about this item

    Keywords

    variational preferences; Uncertainty; risk; common prior; equilibria with short-selling; variational preferences.; Incertitude; risque; croyance commune; équilibre avec ventes à découvert; préférences variationnelles.;

    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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