Multivariate Geometric Tail- And Range-Value-at-Risk

Herrmann, Klaus; Hofert, Marius; Mailhot, Mélina

doi:10.1017/asb.2019.31

Cited by 4 publications

(1 citation statement)

References 24 publications

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“…To this end, it is easy to see why risk measures are constantly evolving. There have been numerous developments in this field, whether it be through establishing ideal properties [3,21,45,46], extensions of univariate measures to higher dimension [11][12][13]22], estimating these measures non-parametrically [4,19], or even the development of new measures [31,32,35,47].…”

Section: Multivariate Risk Measuresmentioning

confidence: 99%

Semi-parametric estimation of multivariate extreme expectiles

Beck

Bernardino

Mailhot

2021

Journal of Multivariate Analysis

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This paper focuses on semi-parametric estimation of multivariate expectiles for extreme levels of risk. Multivariate expectiles and their extremes have been the focus of plentiful research in recent years. In particular, it has been noted that due to the difficulty in estimating these values for elevated levels of risk, an alternative formulation of the underlying optimization problem would be necessary. However, in such a scenario, estimators have only been provided for the limiting cases of tail dependence: independence and comonotonicity. In this paper, we extend the estimation of multivariate extreme expectiles (MEEs) by providing a consistent estimation scheme for random vectors with any arbitrary dependence structure. Specifically, we show that if the upper tail dependence function, tail index, and tail ratio can be consistently estimated, then one would be able to accurately estimate MEEs. The finite-sample performance of this methodology is illustrated using both simulated and real data.

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