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Pareto efficiency for the concave order and multivariate comonotonicity

Author

Listed:
  • Guillaume Carlier

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

  • Rose-Anne Dana

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

  • Alfred Galichon

    (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Guillaume Carlier & Rose-Anne Dana & Alfred Galichon, 2012. "Pareto efficiency for the concave order and multivariate comonotonicity," SciencePo Working papers Main hal-01053549, HAL.
    • Handle: RePEc:hal:spmain:hal-01053549
    DOI: 10.1016/j.jet.2011.11.011
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-01053549
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    References listed on IDEAS

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    1. Dybvig, Philip H, 1988. "Distributional Analysis of Portfolio Choice," The Journal of Business, University of Chicago Press, vol. 61(3), pages 369-393, July.
    2. repec:dau:papers:123456789/2348 is not listed on IDEAS
    3. repec:dau:papers:123456789/343 is not listed on IDEAS
    4. Townsend, Robert M, 1994. "Risk and Insurance in Village India," Econometrica, Econometric Society, vol. 62(3), pages 539-591, May.
    5. repec:dau:papers:123456789/5392 is not listed on IDEAS
    6. repec:dau:papers:123456789/361 is not listed on IDEAS
    7. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    8. 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.
    9. G. Carlier & R. Dana, 2008. "Two-persons efficient risk-sharing and equilibria for concave law-invariant utilities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(2), pages 189-223, August.
    10. Jouini, Elyes & Napp, Clotilde, 2003. "Comonotonic processes," Insurance: Mathematics and Economics, Elsevier, vol. 32(2), pages 255-265, April.
    11. Peleg, Bezalel & Yaari, M E, 1975. "A Price Characterization of Efficient Random Variables," Econometrica, Econometric Society, vol. 43(2), pages 283-292, March.
    12. repec:dau:papers:123456789/344 is not listed on IDEAS
    13. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    14. Jouini, Elyes & Napp, Clotilde, 2003. "Comonotonic processes," Insurance: Mathematics and Economics, Elsevier, vol. 32(2), pages 255-265, April.
    15. Elyès Jouini & Clotilde Napp, 2004. "Conditional comonotonicity," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 27(2), pages 153-166, December.
    16. E. Jouini & W. Schachermayer & N. Touzi, 2008. "Optimal Risk Sharing For Law Invariant Monetary Utility Functions," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 269-292, April.
    17. LeRoy,Stephen F. & Werner,Jan, 2014. "Principles of Financial Economics," Cambridge Books, Cambridge University Press, number 9781107024120, February.
    18. Puccetti, Giovanni & Scarsini, Marco, 2010. "Multivariate comonotonicity," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 291-304, January.
    19. repec:dau:papers:123456789/6697 is not listed on IDEAS
    20. Ludkovski, Michael & Rüschendorf, Ludger, 2008. "On comonotonicity of Pareto optimal risk sharing," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1181-1188, August.
    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.
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    Cited by:

    1. Alfred Galichon & Damien Bosc, 2010. "Extreme dependence for multivariate data," SciencePo Working papers Main hal-03588294, HAL.
    2. Damien Bosc & Alfred Galichon, 2014. "Extreme dependence for multivariate data," SciencePo Working papers Main hal-03470461, HAL.
    3. Jean-Gabriel Lauzier & Liyuan Lin & Ruodu Wang, 2023. "Risk sharing, measuring variability, and distortion riskmetrics," Papers 2302.04034, arXiv.org.
    4. Matteo Burzoni & Alessandro Doldi & Enea Monzio Compagnoni, 2022. "Risk Sharing with Deep Neural Networks," Papers 2212.11752, arXiv.org, revised Jun 2023.
    5. Bernard, C. & De Gennaro Aquino, L. & Vanduffel, S., 2023. "Optimal multivariate financial decision making," European Journal of Operational Research, Elsevier, vol. 307(1), pages 468-483.
    6. Runhuan Feng & Chongda Liu & Stephen Taylor, 2023. "Peer-to-peer risk sharing with an application to flood risk pooling," Annals of Operations Research, Springer, vol. 321(1), pages 813-842, February.

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