Efficient allocations and equilibria with short-selling and incomplete preferences |
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| Institution: | 1. IPAG Business School, CEREMADE, Université Paris-Dauphine, Pl. du maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France;2. IPAG Business School, CNRS, PSE, VCREME, CES, 106-112 Bd de l’Hôpital, 75647 Paris Cedex 13, France;1. Financial Engines, Inc., 1050 Enterprise Way, Sunnyvale, CA 94089, USA;2. Stanford Graduate School of Business, 655 Knight Way, Stanford, CA 94305, USA;3. Retiree Research Center, Financial Engines, Inc., 1050 Enterprise Way, Sunnyvale, CA 94089, USA;1. Paris School of Economics - University Paris 1, CES, 106 bd de l’Hopital, 75013, Paris, France;2. University of La Rochelle (MIA), Avenue Michel Crepeau, 47042, La Rochelle, France;3. University of Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands;1. Center of Economic Research at ETH Zurich (CER-ETH), Switzerland;2. Department of Economics, Maastricht University, Netherlands;1. CNRS (LEM, UMR 8179), France;2. Iéseg School of Management, 3 rue de la Digue, 59000 Lille, France;3. CORE (Université Catholique de Louvain), 34 voie du Roman Pays, 1348 Louvain-la-Neuve, Belgium;4. EM Lyon Business School, 23 avenue Guy de Collongue, 69134 Ecully Cedex, France |
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| Abstract: | This paper reconsiders the theory of existence of efficient allocations and equilibria when consumption sets are unbounded below under the assumption that agents have incomplete preferences. Our model 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. |
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| Keywords: | Uncertainty Risk Risk adjusted prior No arbitrage Equilibrium with short-selling Incomplete preferences |
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