Vector-Valued Multivariate Conditional Value-at-Risk

TL;DR

This paper introduces a novel vector-valued multivariate conditional value-at-risk (VMCVaR) for discrete probability spaces, highlighting its properties and advantages over existing continuous-variable definitions.

Contribution

It proposes a new set-based definition of multivariate CVaR for discrete spaces and analyzes its properties and benefits over prior continuous-variable approaches.

Findings

VMCVaR is a set of vectors suitable for discrete probability spaces.

VMCVaR has advantageous properties compared to existing definitions.

The paper demonstrates the benefits of VMCVaR in discrete settings.

Abstract

In this study, we propose a new definition of multivariate conditional value-at-risk (MCVaR) as a set of vectors for discrete probability spaces. We explore the properties of the vector-valued MCVaR (VMCVaR) and show the advantages of VMCVaR over the existing definitions given for continuous random variables when adapted to the discrete case.