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Weighted Comonotonic Risk Sharing Under Heterogeneous Beliefs

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  • Liu, Haiyan

Abstract

We study a weighted comonotonic risk-sharing problem among multiple agents with distortion risk measures under heterogeneous beliefs. The explicit forms of optimal allocations are obtained, which are Pareto-optimal. A necessary and sufficient condition is given to ensure the uniqueness of the optimal allocation, and sufficient conditions are given to obtain an optimal allocation of the form of excess of loss or full insurance. The optimal allocation may satisfy individual rationality depending on the choice of the weight. When the distortion risk measure is value at risk or tail value at risk, an optimal allocation is generally of the excess-of-loss form. The numerical examples suggest that a risk is more likely to be shared among agents with heterogeneous beliefs, and the introduction of the weight enables us to prioritize some agents as part of a group sharing a risk.

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  • Liu, Haiyan, 2020. "Weighted Comonotonic Risk Sharing Under Heterogeneous Beliefs," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 647-673, May.
    • Handle: RePEc:cup:astinb:v:50:y:2020:i:2:p:647-673_11
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    Cited by:

    1. Boonen, Tim J. & Jiang, Wenjun, 2022. "Bilateral risk sharing in a comonotone market with rank-dependent utilities," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 361-378.
    2. Jean-Gabriel Lauzier & Liyuan Lin & Ruodu Wang, 2023. "Risk sharing, measuring variability, and distortion riskmetrics," Papers 2302.04034, arXiv.org.
    3. Felix-Benedikt Liebrich, 2021. "Risk sharing under heterogeneous beliefs without convexity," Papers 2108.05791, arXiv.org, revised May 2022.

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