On Majorization in Dependence Modeling

Abstract

We apply concepts of majorization theory to derive new insights in the field of extremal dependence structures. In particular, we consider the Rearrangement Algorithm by Puccetti and Rüschendorf, where majorization arguments yield a statement that unifies and extends the existing theory in two ways. The first extension considers convex functions of non-linear risk aggregation and the second allows for non-symmetric cost functions. The article is concluded by computing an example.