Beyond tail median and conditional tail expectation: extreme risk estimation using tail $L^p$−optimisation - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Scandinavian Journal of Statistics Year : 2020

Beyond tail median and conditional tail expectation: extreme risk estimation using tail $L^p$−optimisation

Abstract

The Conditional Tail Expectation is an indicator of tail behaviour that takes into account both the frequency and magnitude of a tail event. However, the asymptotic normality of its empirical estimator requires that the underlying distribution possess a finite variance; this can be a strong restriction in actuarial and financial applications. A valuable alternative is the Median Shortfall, although it only gives information about the frequency of a tail event. We construct a class of tail Lp−medians encompassing the Median Shortfall and Conditional Tail Expectation. For p in (1, 2), a tail Lp−median depends on both the frequency and magnitude of tail events, and its empirical estimator is, within the range of the data, asymptotically normal under a condition weaker than a finite variance. We extrapolate this estimator and another technique to extreme levels using the heavy-tailed framework. The estimators are showcased on a simulation study and on real fire insurance data.
Fichier principal
Vignette du fichier
Scandinavian_main.pdf (432.19 Ko) Télécharger le fichier
Scandinavian_suppl.pdf (3.98 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Format : Other
Comment : Supplementary material (proofs)
Loading...

Dates and versions

hal-01726328 , version 1 (08-03-2018)
hal-01726328 , version 2 (28-01-2019)
hal-01726328 , version 3 (17-07-2019)
hal-01726328 , version 4 (07-11-2019)

Identifiers

Cite

Laurent Gardes, Stéphane Girard, Gilles Stupfler. Beyond tail median and conditional tail expectation: extreme risk estimation using tail $L^p$−optimisation. Scandinavian Journal of Statistics, 2020, 47 (3), pp.922--949. ⟨10.1111/sjos.12433⟩. ⟨hal-01726328v4⟩
499 View
569 Download

Altmetric

Share

Gmail Facebook X LinkedIn More