Journal
OPERATIONS RESEARCH
Volume 66, Issue 6, Pages 1533-1541Publisher
INFORMS
DOI: 10.1287/opre.2018.1736
Keywords
spectral risk measures; coherent risk measures; higher-order risk measures; robust portfolio optimization
Funding
- Canadian Natural Sciences and Engineering Research Council [RGPIN-2014-05602]
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Worst-case risk measures provide a means of calculating the largest value of risk when only partial information of the underlying distribution is available. For popular risk measures such as value-at-risk (VaR) and conditional value-at-risk (CVaR) it is now known that their worst-case counterparts can be evaluated in closed form when only the first two moments are known. We show in this paper that closed-form solutions exist for a general class of law invariant coherent risk measures, which consist of spectral risk measures (and thus CVaR also) as special cases. Moreover, we provide worst-case distributions characterized in terms of risk spectrums, which can take any form of distribution bounded from below. As applications of the closed-form results, new formulas are derived for calculating the worst-case values of higher order risk measures and higher order semideviation, and new robust portfolio optimization models are provided.
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