An elementary proof of the dual representation of Expected Shortfall
Risk Management
2023-06-27 v1 Probability
Mathematical Finance
Abstract
We provide an elementary proof of the dual representation of Expected Shortfall on the space of integrable random variables over a general probability space. Unlike the results in the extant literature, our proof only exploits basic properties of quantile functions and can thus be easily implemented in any graduate course on risk measures. As a byproduct, we obtain a new proof of the subadditivity of Expected Shortfall.
Cite
@article{arxiv.2306.14506,
title = {An elementary proof of the dual representation of Expected Shortfall},
author = {Martin Herdegen and Cosimo Munari},
journal= {arXiv preprint arXiv:2306.14506},
year = {2023}
}