This paper provides a uni¯ed statistical framework for the analysis of distortion riskmeasures (DRM) and of their sensitivities with respect to parameters representing riskaversion and/or pessimism. We derive the general formula for calculating the functionalasymptotic distribution of the...

This paper studies the link between two popular measures of risk, that are the Value-at-Risk (VaR) and the Tail-VaR (TVaR). We study how the TVaR and VaR are related through their risk levels and characterize the underlying distributions under which this relationship is linear. A large portion...

In this thesis, we try to provide a broadeconometric analysis of a class of risk measures, distortion risk measures (DRM). With carefully selected functional form, theValue-at-Risk (VaR) and Tail-VaR (TVaR) are special cases of DRMs. Besides, the DRM also admits interpretation in the sense...

This article introduces a framework to determine and allocate capital reserves to multiple dependent business lines, with or without overall reserve level constraints. The proposed methodology emphasizes the role of the loss function in the validation criterion and its conditional...

We introduce nonparametric estimators of the sensitivity of distortion risk measure with re-spect to portfolio allocation. These estimators are used to derive the estimated e±cient portfolioallocations when distortion risk measures de¯ne the constraints and the objectives, to study...