On Majorization in Dependence Modeling

TL;DR

This paper applies majorization theory to extremal dependence structures, extending the Rearrangement Algorithm to handle convex risk functions and non-symmetric costs, providing new theoretical insights and an illustrative example.

Contribution

It introduces novel majorization-based extensions to the Rearrangement Algorithm, broadening its applicability in dependence modeling.

Findings

Unified and extended theoretical framework

Applicable to convex non-linear risk aggregation

Handles non-symmetric cost functions

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 Rueschendorf, 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.