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Robust bounds in multivariate extremes

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Robust bounds in multivariate extremes. / Engelke, S.; Ivanovs, Jevgenijs.

In: Annals of Applied Probability, Vol. 27, No. 6, 01.12.2017, p. 3706-3734.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

Harvard

Engelke, S & Ivanovs, J 2017, 'Robust bounds in multivariate extremes', Annals of Applied Probability, vol. 27, no. 6, pp. 3706-3734. https://doi.org/10.1214/17-AAP1294

APA

Engelke, S., & Ivanovs, J. (2017). Robust bounds in multivariate extremes. Annals of Applied Probability, 27(6), 3706-3734. https://doi.org/10.1214/17-AAP1294

CBE

Engelke S, Ivanovs J. 2017. Robust bounds in multivariate extremes. Annals of Applied Probability. 27(6):3706-3734. https://doi.org/10.1214/17-AAP1294

MLA

Engelke, S. and Jevgenijs Ivanovs. "Robust bounds in multivariate extremes". Annals of Applied Probability. 2017, 27(6). 3706-3734. https://doi.org/10.1214/17-AAP1294

Vancouver

Engelke S, Ivanovs J. Robust bounds in multivariate extremes. Annals of Applied Probability. 2017 Dec 1;27(6):3706-3734. https://doi.org/10.1214/17-AAP1294

Author

Engelke, S. ; Ivanovs, Jevgenijs. / Robust bounds in multivariate extremes. In: Annals of Applied Probability. 2017 ; Vol. 27, No. 6. pp. 3706-3734.

Bibtex

@article{4f0b343aa59648f8a0a2190c41a4aa17,
title = "Robust bounds in multivariate extremes",
abstract = "Extreme value theory provides an asymptotically justified framework for estimation of exceedance probabilities in regions where few or no observations are available. For multivariate tail estimation, the strength of extremal dependence is crucial and it is typically modeled by a parametric family of spectral distributions. In this work, we provide asymptotic bounds on exceedance probabilities that are robust against misspecification of the extremal dependence model. They arise from optimizing the statistic of interest over all dependence models within some neighborhood of the reference model. A certain relaxation of these bounds yields surprisingly simple and explicit expressions, which we propose to use in applications. We show the effectiveness of the robust approach compared to classical confidence bounds when the model is misspecified. The results are further applied to quantify the effect of model uncertainty on the Value-at-Risk of a financial portfolio.",
keywords = "Convex optimization, Extremal dependence, Model misspecification, Pickands' function, Robust bounds, Stress test",
author = "S. Engelke and Jevgenijs Ivanovs",
year = "2017",
month = dec,
day = "1",
doi = "10.1214/17-AAP1294",
language = "English",
volume = "27",
pages = "3706--3734",
journal = "Annals of Applied Probability",
issn = "1050-5164",
publisher = "Institute of Mathematical Statistics",
number = "6",

}

RIS

TY - JOUR

T1 - Robust bounds in multivariate extremes

AU - Engelke, S.

AU - Ivanovs, Jevgenijs

PY - 2017/12/1

Y1 - 2017/12/1

N2 - Extreme value theory provides an asymptotically justified framework for estimation of exceedance probabilities in regions where few or no observations are available. For multivariate tail estimation, the strength of extremal dependence is crucial and it is typically modeled by a parametric family of spectral distributions. In this work, we provide asymptotic bounds on exceedance probabilities that are robust against misspecification of the extremal dependence model. They arise from optimizing the statistic of interest over all dependence models within some neighborhood of the reference model. A certain relaxation of these bounds yields surprisingly simple and explicit expressions, which we propose to use in applications. We show the effectiveness of the robust approach compared to classical confidence bounds when the model is misspecified. The results are further applied to quantify the effect of model uncertainty on the Value-at-Risk of a financial portfolio.

AB - Extreme value theory provides an asymptotically justified framework for estimation of exceedance probabilities in regions where few or no observations are available. For multivariate tail estimation, the strength of extremal dependence is crucial and it is typically modeled by a parametric family of spectral distributions. In this work, we provide asymptotic bounds on exceedance probabilities that are robust against misspecification of the extremal dependence model. They arise from optimizing the statistic of interest over all dependence models within some neighborhood of the reference model. A certain relaxation of these bounds yields surprisingly simple and explicit expressions, which we propose to use in applications. We show the effectiveness of the robust approach compared to classical confidence bounds when the model is misspecified. The results are further applied to quantify the effect of model uncertainty on the Value-at-Risk of a financial portfolio.

KW - Convex optimization

KW - Extremal dependence

KW - Model misspecification

KW - Pickands' function

KW - Robust bounds

KW - Stress test

UR - http://www.scopus.com/inward/record.url?scp=85037047251&partnerID=8YFLogxK

U2 - 10.1214/17-AAP1294

DO - 10.1214/17-AAP1294

M3 - Journal article

AN - SCOPUS:85037047251

VL - 27

SP - 3706

EP - 3734

JO - Annals of Applied Probability

JF - Annals of Applied Probability

SN - 1050-5164

IS - 6

ER -