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Pareto efficiency for the concave order and multivariate comonotonicity

  • Guillaume Carlier

    (CEntre de REcherches en MAthématiques de la DEcision)

  • Rose-Anna Dana

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

  • Alfred Galichon

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
Contact details of provider: Web page: http://www.sciencespo.fr/
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  2. Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2007. "Optimal Risk Sharing for Law Invariant Monetary Utility Functions," Working Papers halshs-00176606, HAL.
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  4. Carlier Guillaume & Dana Rose-Anne, 2006. "Law invariant concave utility functions and optimization problems with monotonicity and comonotonicity constraints," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 26, July.
  5. Dana, Rose-Anne, 2004. "Market behavior when preferences are generated by second-order stochastic dominance," Economics Papers from University Paris Dauphine 123456789/6697, Paris Dauphine University.
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  9. Rüschendorf Ludger, 2006. "Law invariant convex risk measures for portfolio vectors," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 12, July.
  10. Ludkovski, Michael & Rüschendorf, Ludger, 2008. "On comonotonicity of Pareto optimal risk sharing," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1181-1188, August.
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  13. Philip H. Dybvig, 1987. "Distributional Analysis of Portfolio Choice," Cowles Foundation Discussion Papers 827R, Cowles Foundation for Research in Economics, Yale University, revised Jan 1988.
  14. Jouini, Elyès & Schachermayer, Walter & Touzi, Nizar, 2008. "Optimal Risk Sharing for Law Invariant Monetary Utility Functions," Economics Papers from University Paris Dauphine 123456789/361, Paris Dauphine University.
  15. Elyès Jouini & Clotilde Napp, 2004. "Conditional comonotonicity," Decisions in Economics and Finance, Springer, vol. 27(2), pages 153-166, December.
  16. Elyès Jouini & Clotilde Napp, 2003. "Comonotonic Processes," Post-Print halshs-00167158, HAL.
  17. Dana, Rose-Anne & Carlier, Guillaume, 2006. "Law invariant concave utility functions and optimization problems with monotonicity and comonotonicity constraints," Economics Papers from University Paris Dauphine 123456789/5392, Paris Dauphine University.
  18. Puccetti, Giovanni & Scarsini, Marco, 2010. "Multivariate comonotonicity," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 291-304, January.
  19. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  20. Dana, Rose-Anne & Carlier, Guillaume, 2008. "Two-Persons Efficient Risk-Sharing and Equilibria for Concave Law-Invariant Utilities," Economics Papers from University Paris Dauphine 123456789/2348, Paris Dauphine University.
  21. Zilcha, Itzhak & Chew, Soo Hong, 1990. "Invariance of the efficient sets when the expected utility hypothesis is relaxed," Journal of Economic Behavior & Organization, Elsevier, vol. 13(1), pages 125-131, January.
  22. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  23. Dana, R. A., 2004. "Market behavior when preferences are generated by second-order stochastic dominance," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 619-639, September.
  24. Napp, Clotilde & Jouini, Elyès, 2003. "Comonotonic Processes," Economics Papers from University Paris Dauphine 123456789/343, Paris Dauphine University.
  25. G. Carlier & R. Dana, 2008. "Two-persons efficient risk-sharing and equilibria for concave law-invariant utilities," Economic Theory, Springer, vol. 36(2), pages 189-223, August.
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