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Efficient allocations and equilibria with short-selling and incomplete preferences

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  • Dana, R.A.
  • Le Van, C.

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.

Suggested Citation

  • Dana, R.A. & Le Van, C., 2014. "Efficient allocations and equilibria with short-selling and incomplete preferences," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 101-105.
  • Handle: RePEc:eee:mateco:v:53:y:2014:i:c:p:101-105
    DOI: 10.1016/j.jmateco.2014.06.003
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    References listed on IDEAS

    as
    1. Dana, Rose-Anne & Riedel, Frank, 2013. "Intertemporal equilibria with Knightian uncertainty," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1582-1605.
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    4. Rose-Anne Dana & Cuong Le Van, 2007. "Overlapping sets of priors and the existence of efficient allocations and equilibria for risk measures," Documents de travail du Centre d'Economie de la Sorbonne b07068, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. 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.
    6. Luca Rigotti & Chris Shannon, 2005. "Uncertainty and Risk in Financial Markets," Econometrica, Econometric Society, vol. 73(1), pages 203-243, January.
    7. 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.
    8. Green, Jerry R, 1973. "Temporary General Equilibrium in a Sequential Trading Model with Spot and Futures Transactions," Econometrica, Econometric Society, vol. 41(6), pages 1103-1123, November.
    9. Guillaume Carlier & Rose-Anne Dana, 2013. "Pareto optima and equilibria when preferences are incompletely known," Post-Print hal-00661903, HAL.
    10. Page, Frank Jr., 1996. "Arbitrage and asset prices," Mathematical Social Sciences, Elsevier, vol. 31(3), pages 183-208, June.
    11. 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.
    12. 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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    16. Werner, Jan, 1987. "Arbitrage and the Existence of Competitive Equilibrium," Econometrica, Econometric Society, vol. 55(6), pages 1403-1418, November.
    17. Hart, Oliver D., 1974. "On the existence of equilibrium in a securities model," Journal of Economic Theory, Elsevier, vol. 9(3), pages 293-311, November.
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    19. 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.
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    Citations

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    Cited by:

    1. Hye-Jin Cho, 2016. "Speculative Bubble Burst," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01306093, HAL.
    2. 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.
    3. Hyejin Cho, 2015. "Speculative Bubble Burst," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01184540, HAL.
    4. Chakravarty, Surajeet & Kelsey, David, 2015. "Sharing ambiguous risks," Journal of Mathematical Economics, Elsevier, vol. 56(C), pages 1-8.

    More about this item

    Keywords

    Uncertainty; Risk; Risk adjusted prior; No arbitrage; Equilibrium with short-selling; Incomplete preferences;

    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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