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Pareto efficiency for the concave order and multivariate comonotonicity

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  • Carlier, G.
  • Dana, R.-A.
  • Galichon, A.

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.

Suggested Citation

  • Carlier, G. & Dana, R.-A. & Galichon, A., 2012. "Pareto efficiency for the concave order and multivariate comonotonicity," Journal of Economic Theory, Elsevier, vol. 147(1), pages 207-229.
  • Handle: RePEc:eee:jetheo:v:147:y:2012:i:1:p:207-229
    DOI: 10.1016/j.jet.2011.11.011
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    Cited by:

    1. Carlier, G. & Lachapelle, A., 2011. "A numerical approach for a class of risk-sharing problems," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 1-13, January.
    2. M. Aloqeili & G. Carlier & I. Ekeland, 2014. "Restrictions and identification in a multidimensional risk-sharing problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 409-423, June.
    3. Asimit, Alexandru V. & Badescu, Alexandru M. & Haberman, Steven & Kim, Eun-Seok, 2016. "Efficient risk allocation within a non-life insurance group under Solvency II Regime," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 69-76.
    4. Didrik Flåm, Sjur, 2012. "Coupled projects, core imputations, and the CAPM," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 170-176.
    5. Damien Bosc & Alfred Galichon, 2014. "Extreme dependence for multivariate data," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1187-1199, July.
    6. Kiesel Swen & Rüschendorf Ludger, 2014. "Optimal risk allocation for convex risk functionals in general risk domains," Statistics & Risk Modeling, De Gruyter, vol. 31(3-4), pages 1-31, December.
    7. Alain Chateauneuf & Mina Mostoufi & David Vyncke, 2014. "Multivariate risk sharing and the derivation of individually rational Pareto optima," Working Papers 2014-74, Department of Research, Ipag Business School.
    8. 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.
    9. 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.
    10. 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.
    11. repec:hal:journl:halshs-00942114 is not listed on IDEAS
    12. repec:ipg:wpaper:2014-074 is not listed on IDEAS
    13. Ghossoub, Mario, 2011. "Monotone equimeasurable rearrangements with non-additive probabilities," MPRA Paper 37629, University Library of Munich, Germany, revised 23 Mar 2012.
    14. Sinem Bas & Philippe Bich & Alain Chateauneuf, 2016. "Multidimensional inequalities and generalized quantile functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01313118, HAL.
    15. Chateauneuf, Alain & Mostoufi, Mina & Vyncke, David, 2015. "Multivariate risk sharing and the derivation of individually rational Pareto optima," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 73-78.
    16. Sinem Bas & Philippe Bich & Alain Chateauneuf, 2016. "Multidimensional inequalities and generalized quantile functions," Working Papers hal-01313118, HAL.
    17. repec:eee:ejores:v:267:y:2018:i:2:p:778-790 is not listed on IDEAS
    18. repec:ipg:wpaper:2014-060 is not listed on IDEAS

    More about this item

    Keywords

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

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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