Journal
JOURNAL OF BANKING & FINANCE
Volume 26, Issue 7, Pages 1487-1503Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/S0378-4266(02)00283-2
Keywords
expected shortfall; risk measure; worst conditional expectation; tail conditional expectation; value-at-risk; conditional value-at-risk; tail mean; coherence; quantile; sub-additivity
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Expected shortfall (ES) in several variants has been proposed as remedy for the deficiencies of value-at-risk (VaR) which in general is not a coherent risk measure. In fact, most definitions of ES lead to the same results when applied to continuous loss distributions. Differences may appear when the underlying loss distributions have discontinuities. In this case even the coherence property of ES can get lost unless one took care of the details in its definition. We compare some of the definitions of ES, pointing out that there is one which is robust in the sense of yielding a coherent risk measure regardless of the underlying distributions. Moreover, this ES can be estimated effectively even in cases where the usual estimators for VaR fail. 2002 Elsevier Science B.V. All rights reserved.
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