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....

The tail dependence indexes of a multivariate distribution describe the amount of dependence in the upper right tail or lower left tail of the distribution and can be used to analyse the dependence among extremal random events. This paper examines the tail dependence of multivariate...

This paper is concerned with opportunistic maintenance on a multi-component cumulative damage shock model with stochastically dependent components. A component fails when its cumulative damage exceeds a given threshold, and any such a failure creates a maintenance opportunity, and triggers a...

Tail dependence and conditional tail dependence functions describe, respectively, the tail probabilities and conditional tail probabilities of a copula at various relative scales. The properties as well as the interplay of these two functions are established based upon their homogeneous...