Asymptotic Behaviors Of Tail Distortion Risk Measure And Its Estimation

One of the methods for studying distortion risk measure is to consider WANG distortion risk measure and its variant class under extreme value theory.This type of risk measure contains several indexes,such as,classic quantile VaR,TVaR and CTE,etc.This thesis studies the asymptotic properties of WANG distortion risk measure of and its estimation based on the tail quantile,which are divided into two parts:In the first part,we study the asymptotic properties of the distortion risk measure under different conditions.Firstly,based on linear sum condition,the asymptotic properties of the tail distortion risk measure are obtained by deriving some properties of linear sum.Secondly,the asymptotic behavior of the WANG distortion risk measure is obtained by establishing first-order and second-order asymptotic behaviors for the Frechet,Weibull and Gumbel extreme value distribution.In the second part,we discuss the estimator of the distortion risk measure.Firstly,the estimator of the distortion risk measure is obtained by combining the properties of the tail quantile.Secondly,combining the asymptotic properties obtained in the first part,different estimates of distortion risk measure are obtained.Finally,the properties of the distortion risk measure are obtained by taking estimates of different extreme value parameter ?.