Asymptotic analysis of tail distortion risk measure under the framework of multivariate regular variation

Abstract

Under the framework of multivariate regular variation, we obtain the asymptotic ratio between the tail distortion risk measure for portfolio loss and the sum of value-at-risk for single loss by a different method from the one in Zhu and Li when the confidence level tends to one. In order to illustrate the derived result, a relevant example is given and the corresponding numerical simulation is also carried out.