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Pareto efficiency for the concave order and multivariate comonotonicity

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  • Guillaume Carlier

    (CEntre de REcherches en MAthématiques de la DEcision)

  • Rose-Anna Dana

    (CEntre de REcherches en MAthématiques de la DEcision (CEREMADE))

  • Alfred Galichon

Abstract

This paper studies efficient risk-sharing rules for the concave dominance order. For a univariate risk, it follows from a comonotone dominance principle, due to Landsberger and Meilijson (1994), that efficiency is characterized by a comonotonicity condition. The goal of the paper is to generalize the comonotone dominance principle as well as the equivalence between efficiency and comonotonicity to the multidimensional case. The multivariate case is more involved (in particular because there is no immediate extension of the notion of comonotonicity), and it is addressed by using techniques from convex duality and optimal transportation.

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Paper provided by Sciences Po in its series Sciences Po publications with number info:hdl:2441/5rkqqmvrn4tl22s9mc0p00hch.

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Date of creation: 2012
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Publication status: Published in Journal of Economic Theory, 2012, vol. 147, pp.207-229
Handle: RePEc:spo:wpmain:info:hdl:2441/5rkqqmvrn4tl22s9mc0p00hch

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  16. Carlier Guillaume & Dana Rose-Anne, 2006. "Law invariant concave utility functions and optimization problems with monotonicity and comonotonicity constraints," Statistics & Risk Modeling, De Gruyter, De Gruyter, vol. 24(1/2006), pages 26, July.
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Cited by:
  1. Aloqeili, M. & Carlier, Guillaume & Ekeland, Ivar, 2014. "Restrictions and identification in a multidimensional risk-sharing problem," Economics Papers from University Paris Dauphine 123456789/12413, Paris Dauphine University.
  2. Carlier, G. & Dana, R.-A., 2013. "Pareto optima and equilibria when preferences are incompletely known," Journal of Economic Theory, Elsevier, Elsevier, vol. 148(4), pages 1606-1623.
  3. Didrik Flåm, Sjur, 2012. "Coupled projects, core imputations, and the CAPM," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 170-176.
  4. Alain Chateauneuf & Mina Mostoufi & David Vyncke, 2014. "Multivariate risk sharing and the derivation of individually rational Pareto optima," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00942114, HAL.
  5. G. Carlier & R.-A. Dana, 2014. "Pareto optima and equilibria when preferences are incompletely known," Working Papers, Department of Research, Ipag Business School 2014-060, Department of Research, Ipag Business School.
  6. Ghossoub, Mario, 2011. "Monotone equimeasurable rearrangements with non-additive probabilities," MPRA Paper 37629, University Library of Munich, Germany, revised 23 Mar 2012.

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