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

  • Rose-Anne Dana

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS - Université Paris IX - Paris Dauphine)

  • Cuong Le Van

    ()

    (Axe Economie mathématique et jeux - CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - University of Exeter Business School - University of Exeter Business School - EEP-PSE - Ecole d'Économie de Paris - 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 agents, the more likely are efficient allocations and equilibria to exist.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00470670.

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Date of creation: Nov 2010
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Handle: RePEc:hal:cesptp:halshs-00470670
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