Asymptotic Properties Of Tail Distortion Risk Measure And Its Heavy-tailed Estimation

Distortion risk measure(Wang risk measure)has many good properties compared with other risk measures.The most common research on distortion risk measure is to apply extreme value theory to explore the properties of its tail.In this paper,we discuss the asymptotic properties of tail distortion risk measure and its heavy-tailed estimation.This paper mainly consists of two parts.In the first part,we study the asymptotic properties of the tail distortion risk measure under different regularly variation conditions in the heavy-tailed case.At the same time,we also discuss the asymptotic properties of the tail distortion risk measure under the three extreme attraction fields of Fréchet,Weibull and Gumbel.In the second part,we give a simple heavy-tailed estimator of the tail distortion risk measure class,and prove the consistency and asymptotic normality of the estimator,and study the asymptotic properties of the tail distortion risk measure class under different regularly variation conditions with reference to the first part.