Adjusted Expected Shortfall

Matteo Burzoni, Cosimo Munari and Ruodu Wang
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Matteo Burzoni: Università degli studi di Milano - Dipartimento di Matematica
Cosimo Munari: University of Zurich - Department of Banking and Finance; Swiss Finance Institute
Ruodu Wang: University of Waterloo - Department of Statistics and Actuarial Science

No 20-120, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

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 ESp(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.

Keywords: Convex Risk Measures; Tail Risk; Adjusted Expected Shortfall; Stochastic Dominance; Capital Adequacy; Optimization With Risk Measures (search for similar items in EconPapers)
JEL-codes: C61 D81 G32 (search for similar items in EconPapers)
Pages: 29 pages
Date: 2020-08
New Economics Papers: this item is included in nep-rmg
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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp20120

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