Joint inference on extreme expectiles for multivariate heavy-tailed distributions

TL;DR

This paper develops methods for joint inference on multiple extreme expectiles in multivariate heavy-tailed distributions, providing tools for risk assessment and testing in finance and actuarial science.

Contribution

It introduces a novel approach for simultaneous estimation and inference of several extreme expectiles under dependence, addressing a gap in existing risk measure analysis.

Findings

Accurate confidence regions for extreme expectiles are derived.

A test for equality of multiple extreme expectiles is proposed.

Methods are validated through simulations and real financial data analysis.

Abstract

The notion of expectiles, originally introduced in the context of testing for homoscedasticity and conditional symmetry of the error distribution in linear regression, induces a law-invariant, coherent and elicitable risk measure that has received a significant amount of attention in actuarial and financial risk management contexts. A number of recent papers have focused on the behaviour and estimation of extreme expectile-based risk measures and their potential for risk management. Joint inference of several extreme expectiles has however been left untouched; in fact, even the inference of a marginal extreme expectile turns out to be a difficult problem in finite samples. We investigate the simultaneous estimation of several extreme marginal expectiles of a random vector with heavy-tailed marginal distributions. This is done in a general extremal dependence model where the emphasis is on pairwise dependence between the margins. We use our results to derive accurate confidence regions for extreme expectiles, as well as a test for the equality of several extreme expectiles. Our methods are showcased in a finite-sample simulation study and on real financial data.