| Issue |
ESAIM: PS
Volume 22, 2018
|
|
|---|---|---|
| Page(s) | 163 - 177 | |
| DOI | https://doi.org/10.1051/ps/2018015 | |
| Published online | 16 November 2018 | |
A consistent estimator to the orthant-based tail value-at-risk★,★★
1
Department of Mathematics and Statistics, McGill University,
Montreal,
QC, Canada.
2
Department of Mathematics and Statistics, Concordia University,
Montreal,
QC, Canada.
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Accepted: 13 March 2018
Abstract
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.
Mathematics Subject Classification: 62G05 / 62G20 / 62G32 / 62H12 / 62P05 / 91B30
Key words: Multivariate estimators / risk measures / copulas.
This article has been funded by the Natural Sciences and Engineering Research Council of Canada as well as the Fond de Recherche Nature et Technologies Quebec.
The authors would also like to thank Professor Christian Genest for his numerous helpful comments.
© EDP Sciences, SMAI 2018
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