Tail Distortion Risk Measure For Portfolio With Multivariate Regularly Variation

For the multiplicative background risk model,a distortion-type risk measure is used to measure the tail risk of the portfolio under a scenario probability measure with multivariate regular variation.In this paper,we investigate the tail asymptotics of the portfolio loss?i=1d RiS,where stand-alone-risk vector R=(R1,...,Rd)follows a multivariate regular variation,and is independent of background risk factor S.An ex-plicit asymptotic formula is established for the tail distortion risk measure,and an ex-ample is given to illustrate our obtained results.