# On coherency and other properties of MAXVAR

## TL;DR

This paper investigates the MAXVAR risk measure on L^2 space, providing a straightforward proof of its coherency and averseness, and deriving an explicit formula for its risk envelope based on its relation to CVaR.

## Contribution

It offers the first elementary proof of MAXVAR's properties and explicitly characterizes its risk envelope through its connection to CVaR.

## Key findings

- MAXVAR is coherent and aversive.
- An explicit formula for MAXVAR's risk envelope is derived.
- MAXVAR can be expressed as a convex combination of CVaR.

## Abstract

This paper is concerned with the MAXVAR risk measure on L^2 space. We present an elementary and direct proof of its coherency and averseness. Based on the observation that the MAXVAR measure is a continuous convex combination of the CVaR measure, we provide an explicit formula for the risk envelope of MAXVAR.