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Capital allocation à la Aumann–Shapley for non-differentiable risk measures

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  • Centrone, Francesca
  • Rosazza Gianin, Emanuela

Abstract

We study capital allocation rules satisfying suitable properties for convex and quasi-convex risk measures, by focusing in particular on a family of capital allocation rules based on the dual representation for risk measures and inspired by the Aumann–Shapley allocation principle. These rules extend some well known methods of capital allocation for coherent and convex risk measures to the case of non-Gateaux-differentiable risk measures. We also analyze the properties of the allocation principles here introduced and discuss their suitability in the quasi-convex context.

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  • Centrone, Francesca & Rosazza Gianin, Emanuela, 2018. "Capital allocation à la Aumann–Shapley for non-differentiable risk measures," European Journal of Operational Research, Elsevier, vol. 267(2), pages 667-675.
    • Handle: RePEc:eee:ejores:v:267:y:2018:i:2:p:667-675
    DOI: 10.1016/j.ejor.2017.11.051
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    Cited by:

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    2. Boonen, Tim J. & De Waegenaere, Anja & Norde, Henk, 2020. "A generalization of the Aumann–Shapley value for risk capital allocation problems," European Journal of Operational Research, Elsevier, vol. 282(1), pages 277-287.
    3. Canna, Gabriele & Centrone, Francesca & Rosazza Gianin, Emanuela, 2021. "Haezendonck-Goovaerts capital allocation rules," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 173-185.
    4. Akif Ince & Ilaria Peri & Silvana Pesenti, 2021. "Risk contributions of lambda quantiles," Papers 2106.14824, arXiv.org, revised Nov 2022.
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    6. Grechuk, Bogdan, 2023. "Extended gradient of convex function and capital allocation," European Journal of Operational Research, Elsevier, vol. 305(1), pages 429-437.
    7. Roger J. A. Laeven & Emanuela Rosazza Gianin & Marco Zullino, 2023. "Dynamic Return and Star-Shaped Risk Measures via BSDEs," Papers 2307.03447, arXiv.org, revised Jul 2023.

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