no. 11
Probability theory
About the conditional value at risk of partial sums
[Valeur à risque conditionnelle de sommes de variables aléatoires réelles]

Présenté par : the Editorial Board

Rio, Emmanuel1
1 Université de Versailles, Laboratoire de mathématiques de Versailles, UMR 8100 CNRS, bâtiment Fermat, 45, avenue des États-Unis, 78035 Versailles, France
Comptes Rendus. Mathématique, Tome 355 (2017) no. 11, pp. 1190-1195.

Dans cette note, nous donnons des résultats d'approximation normale pour la CVaR d'une somme de variables aléatoires réelles satisfaisant des hypothèses de moments. Ces résultats sont fondés sur des bornes de type Berry–Esseen pour des coûts de transport dans le théorème limite central ainsi que sur des extensions des inégalités de Cantelli à la CVaR.

In this note, we give normal approximation results for the conditional value at risk (CVaR) of partial sums of random variables satisfying moment assumptions. These results are based on Berry–Esseen-type bounds for transport costs in the central limit theorem and extensions of Cantelli's inequalities to the CVaR.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.10.008
Rio, Emmanuel 1

1 Université de Versailles, Laboratoire de mathématiques de Versailles, UMR 8100 CNRS, bâtiment Fermat, 45, avenue des États-Unis, 78035 Versailles, France 
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Rio, Emmanuel. About the conditional value at risk of partial sums. Comptes Rendus. Mathématique, Tome 355 (2017) no. 11, pp. 1190-1195. doi : 10.1016/j.crma.2017.10.008. http://www.numdam.org/articles/10.1016/j.crma.2017.10.008/

[1] Agnew, R.P. Global versions of the central limit theorem, Proc. Natl. Acad. Sci. USA, Volume 40 (1954), pp. 800-804

[2] Bobkov, S. Berry–Esseen bounds and Edgeworth expansions in the central limit theorem for transport distances, Probab. Theory Relat. Fields (2017) (on line)

[3] Dedecker, J.; Merlevède, F.; Rio, E. Rates of convergence for minimal distances in the central limit theorem under projective criteria, Electron. J. Probab., Volume 14 (2009) no. 35, pp. 978-1011

[4] Fréchet, M. Sur la distance de deux lois de probabilité, Publ. Inst. Stat. Univ. Paris, Volume 6 (1957), pp. 183-198

[5] Gilat, D.; Meilijson, I. A simple proof of a theorem of Blackwell & Dubins on the maximum of a uniformly integrable martingale, Séminaire de Probabilités XXII, Lect. Notes Math., vol. 1321, Springer, Berlin, 1988, pp. 214-216

[6] Hardy, G.; Littlewood, J. A maximal theorem with function-theoretic applications, Acta Math., Volume 54 (1930) no. 1, pp. 81-116

[7] Pinelis, I. 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

[8] Rio, E. Upper bounds for minimal distances in the central limit theorem, Ann. Inst. Henri Poincaré, Probab. Stat., Volume 45 (2009) no. 3, pp. 802-817

[9] E. Rio, About Doob's inequality, entropy and Tchebichef, submitted for publication in Bernoulli (2017).

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