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Efficient allocations and Equilibria with short-selling and Incomplete Preferences

Author

Listed:
  • 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 des Ponts ParisTech - 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)

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.

Suggested Citation

  • Rose-Anne Dana & Cuong Le Van, 2014. "Efficient allocations and Equilibria with short-selling and Incomplete Preferences," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01020646, HAL.
    • Handle: RePEc:hal:cesptp:halshs-01020646
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01020646
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    References listed on IDEAS

    as
    1. Dana, R.A. & Le Van, C., 2010. "Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2186-2202, November.
    2. Rose-Anne Dana & Cuong Le Van, 2007. "Overlapping sets of priors and the existence of efficient allocations and equilibria for risk measures," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00188761, HAL.
    3. Dana, Rose-Anne & Riedel, Frank, 2013. "Intertemporal equilibria with Knightian uncertainty," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1582-1605.
    4. Dana, Rose-Anne & Le Van, Cuong & Magnien, Francois, 1999. "On the Different Notions of Arbitrage and Existence of Equilibrium," Journal of Economic Theory, Elsevier, vol. 87(1), pages 169-193, July.
    5. Guillaume Carlier & Rose-Anne Dana, 2013. "Pareto optima and equilibria when preferences are incompletely known," Post-Print hal-00661903, HAL.
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    7. Luca Rigotti & Chris Shannon, 2005. "Uncertainty and Risk in Financial Markets," Econometrica, Econometric Society, vol. 73(1), pages 203-243, January.
    8. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-1418, November.
    9. Carlier, G. & Dana, R.-A., 2013. "Pareto optima and equilibria when preferences are incompletely known," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1606-1623.
    10. Allouch, Nizar & Le Van, Cuong & Page, Frank Jr., 2002. "The geometry of arbitrage and the existence of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 38(4), pages 373-391, December.
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    14. Rose-Anne Dana & Cuong Le Van, 2010. "Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling," PSE-Ecole d'économie de Paris (Postprint) halshs-00470670, HAL.
    15. Rose-Anne Dana & Cuong Le Van, 2010. "Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling," Post-Print halshs-00470670, HAL.
    16. Rose-Anne Dana & Cuong Le Van, 2010. "Overlapping sets of priors and the existence of efficient allocations and equilibria for risk measures," Post-Print halshs-00308530, HAL.
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    18. Rose-Anne Dana & Cuong Le Van, 2010. "Overlapping sets of priors and the existence of efficient allocations and equilibria for risk measures," PSE-Ecole d'économie de Paris (Postprint) halshs-00308530, HAL.
    19. Page, Frank Jr., 1987. "On equilibrium in Hart's securities exchange model," Journal of Economic Theory, Elsevier, vol. 41(2), pages 392-404, April.
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    Citations

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    Cited by:

    1. Hye-jin Cho, 2016. "Speculative Bubble Burst," Documents de travail du Centre d'Economie de la Sorbonne 16021, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. Hye-Jin Cho, 2016. "Speculative Bubble Burst," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01306093, HAL.
    3. Hyejin Cho, 2015. "Speculative Bubble Burst," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01184540, HAL.
    4. Hyejin Cho, 2015. "Speculative Bubble Burst," Working Papers hal-01184540, HAL.
    5. Chakravarty, Surajeet & Kelsey, David, 2015. "Sharing ambiguous risks," Journal of Mathematical Economics, Elsevier, vol. 56(C), pages 1-8.
    6. Hye-Jin Cho, 2016. "Speculative Bubble Burst," Post-Print halshs-01306093, HAL.
    7. cho, hyejin, 2016. "Speculative Bubble Burst," MPRA Paper 72531, University Library of Munich, Germany.

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    More about this item

    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;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • G1 - Financial Economics - - General Financial Markets

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