On the Concavity of Expected Shortfall
Risk Management
2019-10-03 v1
Abstract
It is well known that Expected Shortfall (also called Average Value-at-Risk) is a convex risk measure, i. e. Expected Shortfall of a convex linear combination of arbitrary risk positions is not greater than a convex linear combination with the same weights of Expected Shortfalls of the same risk positions. In this short paper we prove that Expected Shortfall is a concave risk measure with respect to probability distributions, i. e. Expected Shortfall of a finite mixture of arbitrary risk positions is not lower than the linear combination of Expected Shortfalls of the same risk positions (with the same weights as in the mixture).
Cite
@article{arxiv.1910.00640,
title = {On the Concavity of Expected Shortfall},
author = {Mikhail Tselishchev},
journal= {arXiv preprint arXiv:1910.00640},
year = {2019}
}