Multivariate Quasiconvex Risk Statistics with Scenario Analysis

In this paper, we introduce three new classes of multivariate risk statistics, named multivariate comonotonic quasiconvex risk statistics, multivariate quasiconvex risk statistics and multivariate empirical-law-invariant quasiconvex risk statistics, respectively. Representation results for them are provided by dual method. The results of this paper is not only the generalization of one-dimensional quasiconvex risk statistics, but also the extension of multivariate convex risk statistics.