Asymptotics of the risk concentration based on the tail distortion risk measure

The tail distortion risk measure at level p∈(0,1)p∈(0,1) was introduced in  Zhu and Li (2012) and  Yang (2012), where the parameter pp represents the confidence level. In this paper, we establish the second-order asymptotics of the risk concentration based on the tail distortion risk measure, as p↑1p↑1, for a portfolio of nn independent and identically distributed loss random variables with a common survival function possessing the property of second-order regular variation. Examples are also given.