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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

  • Rose-Anne Dana

    ()

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

  • 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)

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.

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File URL: https://halshs.archives-ouvertes.fr/halshs-00281582v2/document
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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00281582.

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Date of creation: Nov 2009
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Publication status: Published in Documents de travail du Centre d'Economie de la Sorbonne 2008.39 - ISSN : 1955-611X. 2009
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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  21. Rose-Anne Dana, 2002. "On Equilibria when Agents Have Multiple Priors," Annals of Operations Research, Springer, vol. 114(1), pages 105-115, August.
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