Efficient allocations and Equilibria with short-selling and Incomplete Preferences

Rose-Anne Dana () and Cuong Le Van ()
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Rose-Anne Dana: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, IPAG Business School
Cuong Le Van: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, VCREME - Van Xuan Center of Research in Economics, Management and Environment, IPAG Business School

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Abstract: This article reconsiders the theory of existence of efficient allocations and equilibria when consumption sets are unbounded below under the assumption that agents have incomplete preferences. It is motivated by an example in the theory of assets with short-selling where there is risk and ambiguity. Agents have Bewley's incomplete preferences. As an inertia principle is assumed in markets, equilibria are individually rational. It is shown that a necessary and sufficient condition for the existence of an individually rational efficient allocation or of an equilibrium is that the relative interiors of the risk adjusted sets of probabilities intersect. The more risk averse, the more ambiguity averse the agents, the more likely is an equilibrium to exist. The paper then turns to incomplete preferences represented by a family of concave utility functions. Several definitions of efficiency and of equilibrium with inertia are considered. Sufficient conditions and necessary and sufficient conditions are given for the existence of efficient allocations and equilibria with inertia.

Keywords: Uncertainty; risk; risk adjusted prior; no arbitrage; equilibrium with short-selling; incomplete preferences; equilibrium with inertia; Incertitude; risque; risque ajusté; ambiguïté; non arbitrage; équilibre avec ventes à découvert; préférences incomplètes; équilibre avec inertie (search for similar items in EconPapers)
Date: 2014-05
New Economics Papers: this item is included in nep-mic and nep-upt
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01020646v1
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Published in 2014

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