Closed-Form Solutions for Extreme-Case Distortion Risk Measures and Applications to Robust Portfolio Management
29 Pages Posted: 24 Jan 2018 Last revised: 1 Dec 2018
Date Written: January 16, 2018
Extreme-case (worst-case and best-case) risk measures refer to the extreme (maximal and minimal) values for risk measures when only partial information of the underlying risk is available. We obtain closed-form solutions for extreme-case distortion risk measures with the first two moments of the underlying risks available, which completely generalizes the worst-case Value-at-Risk and Expected Shortfall in some classic literature. We characterize the extreme-case distributions that offers great intuition related to the choice of distortion functions.
Keywords: model uncertainty, extreme case, distortion risk measure, robust portfolio selection
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