A consistent estimator to the orthant-based tail value-at-risk

Beck, Nicholas; Mailhot, Mélina

doi:10.1051/ps/2018015

Cited by 3 publications

(2 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Multivariate Risk Measuresmentioning

confidence: 99%

Semi-parametric estimation of multivariate extreme expectiles

Beck

Bernardino

Mailhot

2021

Journal of Multivariate Analysis

Self Cite

View full text Add to dashboard Cite

show abstract

“…Next, we will propose empirical estimators for the lower and upper orthant RVaR, based on the estimators developed by Beck (2015), and provide numerical examples.…”

Section: Empirical Estimator For Multivariate Lower and Upper Orthant...mentioning

confidence: 99%

Range Value-at-Risk: Multivariate and Extreme Values

Bairakdar,

Cao,

Mailhot

2020

Preprint

View full text Add to dashboard Cite

The concept of univariate Range Value-at-Risk, presented by Cont et al. (2010), is extended in the multidimensional setting. Traditional risk measures are not well suited when dealing with heavy-tail distributions and infinite tail expectations. The multivariate definitions of robust truncated tail expectations are provided to overcome this problem. Robustness and other properties as well as empirical estimators are derived. Closed-form expressions and special cases in the extreme value framework are also discussed. Numerical and graphical examples are provided to examine the accuracy of the empirical estimators.

show abstract

Predicting extreme surges from sparse data using a copula‐based hierarchical Bayesian spatial model

et al. 2019

View full text Add to dashboard Cite

A hierarchical Bayesian model is proposed to quantify the magnitude of extreme surges on the Atlantic coast of Canada with limited data. Generalized extreme value distributions are fitted to surges derived from water levels measured at 21 buoys along the coast. The parameters of these distributions are linked together through a Gaussian field whose mean and variance are driven by atmospheric sea‐level pressure and the distance between stations, respectively. This allows for information sharing across the original stations and for interpolation anywhere along the coast. The use of a copula at the data level of the hierarchy further accounts for the dependence between locations, allowing for inference beyond a site‐by‐site basis. It is shown how the extreme surges derived from the model can be combined with the tidal process to predict potentially catastrophic water levels.

show abstract

A consistent estimator to the orthant-based tail value-at-risk

Cited by 3 publications

References 17 publications

Semi-parametric estimation of multivariate extreme expectiles

Semi-parametric estimation of multivariate extreme expectiles

Range Value-at-Risk: Multivariate and Extreme Values

Predicting extreme surges from sparse data using a copula‐based hierarchical Bayesian spatial model

Contact Info

Product

Resources

About