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Inf-convolution and optimal allocations for mixed-VaRs

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  • Xia, Zichao
  • Zou, Zhenfeng
  • Hu, Taizhong

Abstract

A mixed Value-at-Risk (VaR) is a two-parameter quantile-based risk measure, which is a convex combination of left-VaR and right-VaR. In this paper, we investigate optimal allocations in a risk sharing problem where the objectives of agents are mixed-VaRs. Explicit formulas of the inf-convolution and Pareto optimal allocations are obtained. The worst-case mixed VaR under model uncertainty is also presented.

Suggested Citation

  • Xia, Zichao & Zou, Zhenfeng & Hu, Taizhong, 2023. "Inf-convolution and optimal allocations for mixed-VaRs," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 156-164.
    • Handle: RePEc:eee:insuma:v:108:y:2023:i:c:p:156-164
    DOI: 10.1016/j.insmatheco.2022.12.001
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    References listed on IDEAS

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    3. Jean-Gabriel Lauzier & Liyuan Lin & Ruodu Wang, 2023. "Pairwise counter-monotonicity," Papers 2302.11701, arXiv.org, revised May 2023.
    4. Lauzier, Jean-Gabriel & Lin, Liyuan & Wang, Ruodu, 2023. "Pairwise counter-monotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 279-287.

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    More about this item

    Keywords

    Quantile; Risk measure; Risk sharing; Model uncertainty;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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