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

See all articles by Wenhao Zhu

Wenhao Zhu

affiliation not provided to SSRN

Hui Shao

National University of Singapore (NUS) - Risk Management Institute

Date Written: January 16, 2018

Abstract

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

Suggested Citation

Zhu, Wenhao and Shao, Hui, Closed-Form Solutions for Extreme-Case Distortion Risk Measures and Applications to Robust Portfolio Management (January 16, 2018). Available at SSRN: https://ssrn.com/abstract=3103458 or http://dx.doi.org/10.2139/ssrn.3103458

Wenhao Zhu

affiliation not provided to SSRN

Hui Shao (Contact Author)

National University of Singapore (NUS) - Risk Management Institute ( email )

21 Heng Mui Keng Terrace
Level 4
Singapore, 119613
Singapore

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