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

Author

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  • Rose-Anne Dana

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique)

  • Cuong Le Van

    () (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, University of Exeter Business School - University of Exeter Business School, PSE - Paris School of Economics)

Abstract

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.

Suggested Citation

  • Rose-Anne Dana & Cuong Le Van, 2010. "Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00470670, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00470670 DOI: 10.1016/j.jet.2010.08.002 Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00470670
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Ha-Huy, Thai & Le Van, Cuong & Nguyen, Manh-Hung, 2016. "Arbitrage and asset market equilibrium in infinite dimensional economies with short-selling and risk-averse expected utilities," Mathematical Social Sciences, Elsevier, pages 30-39.
    2. Stefano Bosi & Patrice Fontaine & Cuong Le Van, 2013. "Equilibrium existence in the international asset and good markets," Working Papers 2013-3, Department of Research, Ipag Business School.
    3. repec:eee:mateco:v:73:y:2017:i:c:p:44-53 is not listed on IDEAS
    4. 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.
    5. Thai Ha-Huy & Cuong Le Van & Frank Page & Myrna Wooders, 2017. "No-arbitrage and Equilibrium in Finite Dimension: A General Result," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01529663, HAL.
    6. R.A Dana & C. Le Van, 2014. "Efficient allocations and Equilibria with short," Working Papers 2014-61, Department of Research, Ipag Business School.
    7. G. Carlier & R.-A. Dana & R.-A. Dana, 2014. "Pareto optima and equilibria when preferences are incompletely known," Working Papers 2014-60, Department of Research, Ipag Business School.
    8. Ha-Huy, Thai & Le Van, Cuong & Nguyen, Manh-Hung, 2011. "Arbitrage and asset market equilibrium in infinite dimensional economies with risk-averse expected utilities," LERNA Working Papers 11.12.346, LERNA, University of Toulouse.
    9. Grechuk, Bogdan, 2015. "The center of a convex set and capital allocation," European Journal of Operational Research, Elsevier, vol. 243(2), pages 628-636.
    10. repec:hal:journl:halshs-01020646 is not listed on IDEAS
    11. repec:ipg:wpaper:201420 is not listed on IDEAS

    More about this item

    Keywords

    Variational preferences; risk; common prior; equilibria with shortselling; Uncertainty;

    JEL classification:

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

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