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

Rose-Anne Dana (1) , Cuong Le Van (2, 3, 4)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 CES - Centre d'économie de la Sorbonne
3 University of Exeter Business School
4 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 agents, the more likely are efficient allocations and equilibria to exist.

Mots clés: Uncertainty; risk; common prior; equilibria with shortselling; Variational preferences

Domaines: Economies et finances

Rose-Anne Dana, Cuong Le Van. Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling. Journal of Economic Theory, 2010, 145 (6), pp.2186-2202. ⟨10.1016/j.jet.2010.08.002⟩. ⟨halshs-00470670⟩