On the Concavity of Expected Shortfall

Mikhail Tselishchev

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arXiv · 1910.00640

On the Concavity of Expected Shortfall

Mikhail Tselishchev

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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).

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Mikhail Tselishchev. 2019-10-01. On the Concavity of Expected Shortfall. https://arxiv.org/abs/1910.00640

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