Consider a portfolio of n identically distributed risks with dependence structure modeled by an Archimedean survival copula. Wüthrich (2003) and Alink et al. (2004) proved that the probability of a large aggregate loss scales like the probability of a large individual loss, times a...

The quantification of diversification benefits due to risk aggregation has received more attention in the recent literature. In this paper, we establish second-order expansions of the risk concentration based on the risk measure of conditional tail expectation for a portfolio of n independent...

The tail distortion risk measure at level p∈(0,1) was introduced in  Zhu and Li (2012) and  Yang (2012), where the parameter p 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...

Karamata’s theorem is well known, which examines the integral properties of regular variation functions. In this paper, we obtain the second-order version of Karamata’s theorem, and give its one application in characterizing the second-order regular variation property of a survival function...