Irène Gijbels

Title

Quantiles, expectiles, risk measures and beyond

Abstract

This talk starts by discussing a class of functionals that presents a framework in which well-known concepts such as for example quantiles, expectiles, expected shortfall find their place. After introducing the class of functionals and the basic properties, we discuss estimation of the functionals, mention statistical properties (convergence, asymptotic normality, ...), and demonstrate briefly the practical use. The functionals allow to study in one single track several concepts/risk measures. In a next step we move from individual components (variables) to global systems (think of portfolios) consisting of several individual components, often with dependence among them. The studied functionals, together with a copula-approach to describe dependencies, then leads to the investigation of risks of portfolios (and risk diversification). Of particular interest is what are strategies to be chosen when there is a given natural clustering between various elements of the portfolio. A final topic that we touch upon is when the variable of interest is influenced by a set of covariates, i.e. when dealing with a regression context.

Keywords

• Copulas
• Estimation
• Risk measures
• Portfolios