B1515
Title: Accurate Gaussian inference about extreme expectiles and application in cyber risk
Authors: Antoine Usseglio-Carleve - Avignon Université (France) [presenting]
Gilles Stupfler - University of Angers (France)
Abdelaati Daouia - Toulouse School of Economics (France)
Abstract: The expectile is a prime candidate for being a standard risk measure in actuarial and financial contexts, for its ability to recover information about probabilities and typical behaviour of extreme values, as well as its excellent axiomatic properties. A series of recent papers have focused on expectile estimation at extreme levels, with a view to gathering essential information about low probability. These high-impact events are of most interest to risk managers. The obtention of accurate confidence intervals for extreme expectiles is paramount in any decision process in which they are involved. However, actual inference on these tail risk measures is still a difficult question due to their least squares nature and sensitivity to tail heaviness. The focus is on asymptotic Gaussian inference about tail expectiles in the challenging context of heavy-tailed observations. An in-depth analysis of the proofs of asymptotic normality results is used for two classes of extreme expectile estimators to derive bias-reduced and variance-corrected Gaussian confidence intervals. Unlike previous attempts in the literature, these are well-rooted in statistical theory and can accommodate underlying distributions that display a wide range of tail behaviours. A large-scale simulation study and an application in cyber risk confirm the versatility of the proposed technique.
