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Adjusted Expected Shortfall

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  • Matteo Burzoni
  • Cosimo Munari
  • Ruodu Wang

Abstract

We introduce and study the main properties of a class of convex risk measures that refine Expected Shortfall by simultaneously controlling the expected losses associated with different portions of the tail distribution. The corresponding adjusted Expected Shortfalls quantify risk as the minimum amount of capital that has to be raised and injected into a financial position $X$ to ensure that Expected Shortfall $ES_p(X)$ does not exceed a pre-specified threshold $g(p)$ for every probability level $p\in[0,1]$. Through the choice of the benchmark risk profile $g$ one can tailor the risk assessment to the specific application of interest. We devote special attention to the study of risk profiles defined by the Expected Shortfall of a benchmark random loss, in which case our risk measures are intimately linked to second-order stochastic dominance.

Suggested Citation

  • Matteo Burzoni & Cosimo Munari & Ruodu Wang, 2020. "Adjusted Expected Shortfall," Papers 2007.08829, arXiv.org, revised Aug 2021.
    • Handle: RePEc:arx:papers:2007.08829
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    References listed on IDEAS

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    Cited by:

    1. Martin Herdegen & Nazem Khan, 2022. "$\rho$-arbitrage and $\rho$-consistent pricing for star-shaped risk measures," Papers 2202.07610, arXiv.org, revised Feb 2024.

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