Extreme M-quantiles as risk measures: From $L^{1}$ to $L^{p}$ optimization

By Abdelaati Daouia, Stéphane Girard, Gilles Stupfler. Bernoulli, 2019

56 citations recorded by the source corpus.

The class of quantiles lies at the heart of extreme-value theory and is one of the basic tools in risk management. The alternative family of expectiles is based on squared rather than absolute error loss minimization. It has recently been receiving a lot of attention in actuarial science, econometrics and statistical finance. Both quantiles and expectiles can be embedded in a more general class of M-quantiles by means of Lp optimization. These generalized Lp-quantiles steer an advantageous middle course between ordinary quantiles and expectiles without sacrificing their virtues too much for 1 p 2. In this paper, we investigate their estimation from the perspective of extreme values in the class of heavy-tailed distributions. We construct estimators of the intermediate Lp-quantiles and establish their asymptotic normality in a dependence framework motivated by financial and actuarial applications, before extrapolating these estimates to the very far tails. We also investigate the potential of extreme Lp-quantiles as a tool for estimating the usual quantiles and expectiles themselves. We show the usefulness of extreme Lp-quantiles and elaborate the choice of p through applications to some simulated and financial real data.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5178fdc59b7304de0f537db6ed5d94219b4d9d92

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Gilles Stupfler
2. Abdelaati Daouia
3. Irène Gijbels
4. Stéphane Girard

In Management Science and Operations Research

1. Irène Gijbels
2. Abdelaati Daouia
3. Gilles Stupfler
4. Léopold Simar
5. Paul Wilson

In Statistics and Probability

1. Irène Gijbels
2. Gilles Stupfler
3. Abdelaati Daouia
4. Peter Hall
5. Aurore Delaigle
6. Léopold Simar
7. A. Meister

Citations in the corpus

• Extremiles: A New Perspective on Asymmetric Least Squares (2018, result): “Although the time series case goes beyond the scope of the present article, the recent analysis of Daouia, Girard, and Stupfler (2017) suggests that it may be possible to extend the results obtained here under appropriate mixing conditions on the underlying series.”