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In this paper, we address the estimation of multivariate value-at-risk (VaR) and tail value-at-risk (TVaR). We recall definitions for the bivariate lower and upper orthant VaR and bivariate lower and upper orthant TVaR, presented in Cossette et al. [Eur. Actuar. J. 3 (2013) 321–357 or Methodol. Comput. Appl. Probab. (2014) 1–22]. Here, we present estimators for both these measures extended to an arbitrary dimension d ≥ 2 and establish the consistency of our estimator for the lower and upper orthant TVaR in any dimension. We demonstrate these results by providing numerical examples that compare our estimator to theoretical results for both simulated and real data.
Beck, Nicholas 1 ; Mailhot, Mélina 1
@article{PS_2018__22__163_0,
author = {Beck, Nicholas and Mailhot, M\'elina},
title = {A consistent estimator to the orthant-based tail value-at-risk},
journal = {ESAIM: Probability and Statistics},
pages = {163--177},
publisher = {EDP-Sciences},
volume = {22},
year = {2018},
doi = {10.1051/ps/2018015},
mrnumber = {3877330},
zbl = {1409.62206},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2018015/}
}
TY - JOUR AU - Beck, Nicholas AU - Mailhot, Mélina TI - A consistent estimator to the orthant-based tail value-at-risk JO - ESAIM: Probability and Statistics PY - 2018 SP - 163 EP - 177 VL - 22 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ps/2018015/ DO - 10.1051/ps/2018015 LA - en ID - PS_2018__22__163_0 ER -
%0 Journal Article %A Beck, Nicholas %A Mailhot, Mélina %T A consistent estimator to the orthant-based tail value-at-risk %J ESAIM: Probability and Statistics %D 2018 %P 163-177 %V 22 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ps/2018015/ %R 10.1051/ps/2018015 %G en %F PS_2018__22__163_0
Beck, Nicholas; Mailhot, Mélina. A consistent estimator to the orthant-based tail value-at-risk. ESAIM: Probability and Statistics, Tome 22 (2018), pp. 163-177. doi: 10.1051/ps/2018015
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