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...

A distortion risk measure used in finance and insurance is defined as the expected value of potential loss under a scenario probability measure. In this paper, the tail distortion risk measure is introduced to assess tail risks of excess losses modeled by the right tails of loss distributions....

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...

Asymptotic results are obtained for several conditional measures of association. The chosen random variables are the first two order statistics and the total sum within a random sum. Many of the results have confirmed the “one-jump” property of the risk model. Non-trivial limits are...

Consider a renewal risk model in which claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure described via the conditional distribution of the inter-arrival time given the...