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An elementary proof of the dual representation of Expected Shortfall

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  • Martin Herdegen
  • Cosimo Munari

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.

Suggested Citation

  • Martin Herdegen & Cosimo Munari, 2023. "An elementary proof of the dual representation of Expected Shortfall," Papers 2306.14506, arXiv.org.
    • Handle: RePEc:arx:papers:2306.14506
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    References listed on IDEAS

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