IDEAS home Printed from https://ideas.repec.org/p/msh/ebswps/2024-18.html
   My bibliography  Save this paper

Risk Sharing, Measuring Variability, and Distortion Riskmetrics

Author

Listed:
  • Jean-Gabriel Lauzier
  • Liyuan Lin
  • Ruodu Wang

Abstract

We address the problem of sharing risk among agents with preferences modelled by a generalclass of comonotonic additive and law-invariant functionals that need not be either monotoneor convex. Such functionals are called distortion riskmetrics, which include many statisticalmeasures of risk and variability used in portfolio optimization and insurance. The set of Pareto Optimal allocations is characterized under various settings of general or comonotonic risk sharing problems. We solve explicitly Pareto-optimal allocations among agents using the Gini deviation, the mean-median deviation, or the inter-quantile difference as the relevant variability measures. The latter is of particular interest, as optimal allocations are not comonotonic in the presenceof inter-quantile difference agents; instead, the optimal allocation features a mixture of pairwise counter-monotonic structures, showing some patterns of extremal negative dependence.

Suggested Citation

  • Jean-Gabriel Lauzier & Liyuan Lin & Ruodu Wang, 2024. "Risk Sharing, Measuring Variability, and Distortion Riskmetrics," Monash Econometrics and Business Statistics Working Papers 18/24, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2024-18
    as

    Download full text from publisher

    File URL: https://www.monash.edu/business/ebs/research/publications/ebs/2024/wp18-2024.pdf
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    Signed Choquet Integrals; Risk Sharing; Â Inter-Quantile Difference; Â Variability Measures; Pairwise Counter-Monotonicity;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:msh:ebswps:2024-18. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Professor Xibin Zhang (email available below). General contact details of provider: https://edirc.repec.org/data/dxmonau.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.