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

El Methni, Jonathan; Stupfler, Gilles

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: https://nottingham-repository.worktribe.com/output/929455
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S2452306217300151
• Contract Date: Mar 9, 2017