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Technical Note—Closed-Form Solutions for Worst-Case Law Invariant Risk Measures with Application to Robust Portfolio Optimization.
- Source :
- Operations Research; Nov/Dec2018, Vol. 66 Issue 6, p1533-1541, 9p, 1 Graph
- Publication Year :
- 2018
-
Abstract
- 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. The online appendix is available at https://doi.org/10.1287/opre.2018.1736. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0030364X
- Volume :
- 66
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- Operations Research
- Publication Type :
- Academic Journal
- Accession number :
- 133768914
- Full Text :
- https://doi.org/10.1287/opre.2018.1736