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Risk sharing, measuring variability, and distortion riskmetrics

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  • Jean-Gabriel Lauzier
  • Liyuan Lin
  • Ruodu Wang

Abstract

We address the problem of sharing risk among agents with preferences modelled by a general class of comonotonic additive and law-based functionals that need not be either monotone or convex. Such functionals are called distortion riskmetrics, which include many statistical measures 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 presence of 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, 2023. "Risk sharing, measuring variability, and distortion riskmetrics," Papers 2302.04034, arXiv.org.
    • Handle: RePEc:arx:papers:2302.04034
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    References listed on IDEAS

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    Cited by:

    1. Mario Ghossoub & Qinghua Ren & Ruodu Wang, 2024. "Counter-monotonic risk allocations and distortion risk measures," Papers 2407.16099, arXiv.org.
    2. Jean-Gabriel Lauzier & Liyuan Lin & Ruodu Wang, 2023. "Pairwise counter-monotonicity," Papers 2302.11701, arXiv.org, revised May 2023.
    3. Peng Liu & Andreas Tsanakas & Yunran Wei, 2024. "Risk sharing with Lambda value at risk under heterogeneous beliefs," Papers 2408.03147, arXiv.org, revised Sep 2024.
    4. Jean-Gabriel Lauzier & Liyuan Lin & Ruodu Wang, 2024. "Negatively dependent optimal risk sharing," Papers 2401.03328, arXiv.org.

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