• 15/02/2023 - 15h - CLAV Anfiteatro 1
Lígia Henriques-Rodrigues, Universidade de Évora
In the field of statistical extreme value theory, risk is generally expressed either by  the value at risk at a level q (VaR_q), the size of the loss occurred with a  fixed probability, q, the upper (1-q)-quantile of the loss function, or by the conditional tail expectation (CTE), defined as
CTE_q  =E(X|X>VaR_q), q\in(0,1). We  consider heavy-tailed models, i.e. Pareto-type underlying CDFs, with a positive extreme value index (EVI), quite common in many areas of application. For these Pareto-type  models, the classical EVI-estimators are the Hill (H) estimators, the average of the k log-excesses over a threshold X_{n-k:n}.
The Hill estimator is crucial for the semi-parametric estimation of both the VaR and the CTE. We present improvements in the performance of the aforementioned VaR- and CTE-estimators, through the use of a reliable EVI-estimator based on generalized means and possibly reduced-bias.
(Joint works with Maria Ivette Gomes, Frederico Caeiro and Fernanda Figueiredo.)
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