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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

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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: ftp://mse.univ-paris1.fr/pub/mse/CES2008/B08039.pdf
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Paper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number b08039.

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Length: 30 pages
Date of creation: May 2008
Date of revision: Nov 2009
Handle: RePEc:mse:cesdoc:b08039

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Keywords: Uncertainty; risk; common prior; equilibria with short-selling; variational preferences.;

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