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Comptes Rendus. Mathématique
Probability theory
Upper bounds for superquantiles of martingales
Comptes Rendus. Mathématique, Volume 359 (2021) no. 7, pp. 813-822.

Let (M n ) n be a discrete martingale in L p for p in ]1,2] or p=3. In this note, we give upper bounds on the superquantiles of M n and the quantiles and superquantiles of M n * =max(M 0 ,M 1 ,...,M n ).

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DOI: https://doi.org/10.5802/crmath.207
Classification: 60E15
Emmanuel Rio 1

1. Université de Versailles, Laboratoire de mathématiques, UMR 8100 CNRS, Bâtiment Fermat, 45 Avenue des Etats-Unis, F-78035 Versailles, France.
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Emmanuel Rio. Upper bounds for superquantiles of martingales. Comptes Rendus. Mathématique, Volume 359 (2021) no. 7, pp. 813-822. doi : 10.5802/crmath.207. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.207/

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[11] Iosif Pinelis An Optimal Three-Way Stable and Monotonic Spectrum of Bounds on Quantiles: A Spectrum of Coherent Measures of Financial Risk and Economic Inequality, Risks, Volume 2 (2014) no. 3, pp. 349-392 | Article

[12] Iosif Pinelis Best possible bounds of the von Bahr–Esseen type, Ann. Funct. Anal., Volume 6 (2015) no. 4, pp. 1-29 | Article | MR 3365979 | Zbl 1319.60036

[13] Iosif Pinelis Exact Rosenthal-type bounds, Ann. Probab., Volume 43 (2015) no. 5, pp. 2511-2544 | MR 3395468 | Zbl 1336.60033

[14] Emmanuel Rio Exponential inequalities for weighted sums of bounded random variables, Electron. Commun. Probab., Volume 20 (2015), 77, 10 pages | MR 3417449 | Zbl 1328.60054

[15] Emmanuel Rio About Doob’s inequality, entropy and Tchebichef, Electron. Commun. Probab., Volume 23 (2018), 78, 12 pages | MR 3873785 | Zbl 1401.60027

[16] Pafnutiĭ L. Tchebichef Sur les valeurs limites des intégrales, Liouville J., Volume 19 (1874), pp. 157-160 | Zbl 0.0180.02

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