A comparison of techniques for dynamic multivariate risk measures

TL;DR

This paper compares four approaches to dynamic multivariate risk measures, analyzing their assumptions, properties, and how they relate to each other in terms of primal and dual representations and time consistency.

Contribution

It provides a comprehensive comparison of different methods for dynamic multivariate risk measures, clarifying their assumptions and relationships.

Findings

Conditions under which approaches coincide

Comparison of primal and dual representations

Analysis of time consistency properties

Abstract

This paper contains an overview of results for dynamic multivariate risk measures. We provide the main results of four different approaches. We will prove under which assumptions results within these approaches coincide, and how properties like primal and dual representation and time consistency in the different approaches compare to each other.