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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. Matteo Burzoni & Alessandro Doldi & Enea Monzio Compagnoni, 2022. "Risk Sharing with Deep Neural Networks," Papers 2212.11752, arXiv.org, revised Jun 2023.
    2. Alfred Galichon & Damien Bosc, 2010. "Extreme dependence for multivariate data," SciencePo Working papers Main hal-03588294, HAL.
    3. 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.
    4. Damien Bosc & Alfred Galichon, 2014. "Extreme dependence for multivariate data," SciencePo Working papers Main hal-03470461, HAL.
    5. 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.
    6. Jean-Gabriel Lauzier & Liyuan Lin & Ruodu Wang, 2023. "Risk sharing, measuring variability, and distortion riskmetrics," Papers 2302.04034, arXiv.org.

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