Multivariate extensions of expectiles risk measures

TL;DR

This paper introduces multivariate expectiles, a new family of elicitable risk measures, discusses their properties, and proposes a stochastic approximation method for their computation.

Contribution

It presents the first construction of multivariate expectiles, analyzes their coherence, and develops a stochastic approximation algorithm.

Findings

Multivariate expectiles are elicitable risk measures.

The paper establishes coherence properties of these measures.

A stochastic approximation method for multivariate expectiles is proposed.

Abstract

This paper is devoted to the introduction and study of a new family of multivariate elicitable risk measures. We call the obtained vector-valued measures multivariate expectiles. We present the different approaches used to construct our measures. We discuss the coherence properties of these multivariate expectiles. Furthermore, we propose a stochastic approximation tool of these risk measures.