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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.

Keywords

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}
}