A consistent estimator to the orthant-based tail value-at-risk
ESAIM: Probability and Statistics, Tome 22 (2018), pp. 163-177

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.

DOI : 10.1051/ps/2018015
Classification : 62G05, 62G20, 62G32, 62H12, 62P05, 91B30
Keywords: Multivariate estimators, risk measures, copulas.

Beck, Nicholas 1 ; Mailhot, Mélina 1

1 
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     title = {A consistent estimator to the orthant-based tail value-at-risk},
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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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