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Pareto efficiency for the concave order and multivariate comonotonicity

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  • Galichon, Alfred
  • Dana, Rose-Anne
  • Carlier, Guillaume

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) [27], 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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File URL: http://basepub.dauphine.fr/xmlui/bitstream/123456789/9713/2/Dana-paper.pdf
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Bibliographic Info

Paper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/9713.

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Date of creation: 2012
Date of revision:
Publication status: Published in Journal of Economic Theory, 2012, Vol. 147, no. 1. pp. 207-229.Length: 22 pages
Handle: RePEc:dau:papers:123456789/9713

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Keywords: Multivariate risk-sharing; Efficiency; Comonotonicity; Stochastic dominance; Concave order;

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References

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  1. Ludkovski, Michael & Rüschendorf, Ludger, 2008. "On comonotonicity of Pareto optimal risk sharing," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1181-1188, August.
  2. Clotilde Napp & Elyès Jouini, 2005. "Conditional Comonotonicity," Post-Print halshs-00151516, HAL.
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  8. 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.
  9. Napp, Clotilde & Jouini, Elyès, 2004. "Conditional Comonotonicity," Economics Papers from University Paris Dauphine 123456789/344, Paris Dauphine University.
  10. 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.
  11. Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2007. "Optimal Risk Sharing for Law Invariant Monetary Utility Functions," Working Papers halshs-00176606, HAL.
  12. 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.
  13. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  14. Napp, Clotilde & Jouini, Elyès, 2003. "Comonotonic Processes," Economics Papers from University Paris Dauphine 123456789/343, Paris Dauphine University.
  15. Peleg, Bezalel & Yaari, M E, 1975. "A Price Characterization of Efficient Random Variables," Econometrica, Econometric Society, vol. 43(2), pages 283-92, March.
  16. 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.
  17. Jouini, Elyes & Napp, Clotilde, 2003. "Comonotonic processes," Insurance: Mathematics and Economics, Elsevier, vol. 32(2), pages 255-265, April.
  18. 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.
  19. Puccetti, Giovanni & Scarsini, Marco, 2010. "Multivariate comonotonicity," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 291-304, January.
  20. 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.
  21. LeRoy,Stephen F. & Werner,Jan, 2001. "Principles of Financial Economics," Cambridge Books, Cambridge University Press, number 9780521586054.
  22. Zephyr, 2010. "The city," City, Taylor & Francis Journals, vol. 14(1-2), pages 154-155, February.
  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. Rüschendorf Ludger, 2006. "Law invariant convex risk measures for portfolio vectors," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 12, July.
  25. 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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Citations

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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, vol. 148(4), pages 1606-1623.
  3. Ghossoub, Mario, 2011. "Monotone equimeasurable rearrangements with non-additive probabilities," MPRA Paper 37629, University Library of Munich, Germany, revised 23 Mar 2012.
  4. G. Carlier & R.-A. Dana, 2014. "Pareto optima and equilibria when preferences are incompletely known," Working Papers 2014-060, Department of Research, Ipag Business School.
  5. Alain Chateauneuf & Mina Mostoufi & David Vyncke, 2014. "Multivariate risk sharing and the derivation of individually rational Pareto optima," Working Papers 2014-074, Department of Research, Ipag Business School.
  6. Didrik Flåm, Sjur, 2012. "Coupled projects, core imputations, and the CAPM," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 170-176.

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