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Improved estimators of extreme Wang distortion risk measures for very heavy-tailed distributions

El Methni, Jonathan; Stupfler, Gilles

Authors

Jonathan El Methni

Gilles Stupfler



Abstract

A general way to study the extremes of a random variable is to consider the family of its Wang distortion risk measures. This class of risk measures encompasses several indicators such as the classical quantile/Value-at-Risk, the Tail-Value-at-Risk and Conditional Tail Moments. Trimmed and winsorised versions of the empirical counterparts of extreme analogues of Wang distortion risk measures are considered. Their asymptotic properties are analysed, and it is shown that it is possible to construct corrected versions of trimmed or winsorised estimators of extreme Wang distortion risk measures who appear to perform overall better than their standard empirical counterparts in difficult finite-sample situations when the underlying distribution has a very heavy right tail. This technique is showcased on a set of real fire insurance data.

Citation

El Methni, J., & Stupfler, G. (2018). Improved estimators of extreme Wang distortion risk measures for very heavy-tailed distributions. Econometrics and Statistics, 6, https://doi.org/10.1016/j.ecosta.2017.03.002

Journal Article Type Article
Acceptance Date Mar 6, 2017
Online Publication Date Mar 10, 2017
Publication Date Apr 30, 2018
Deposit Date Mar 9, 2017
Publicly Available Date Mar 10, 2017
Journal Econometrics and Statistics
Electronic ISSN 2452-3062
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 6
DOI https://doi.org/10.1016/j.ecosta.2017.03.002
Keywords Asymptotic normality, Extreme value statistics, Heavy-tailed distribution, Trimming, Wang distortion risk measure, Winsorising
Public URL http://eprints.nottingham.ac.uk/id/eprint/41195
Publisher URL http://www.sciencedirect.com/science/article/pii/S2452306217300151
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0





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