An elementary proof of the dual representation of Expected Shortfall

Martin Herdegen and Cosimo Munari

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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.

Date: 2023-06
New Economics Papers: this item is included in nep-rmg
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