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Mean-Covariance Robust Risk Measurement

Author

Listed:
  • Viet-Anh Nguyen

    (Ecole Polytechnique Federale de Lausanne - MTEI)

  • Soroosh Shafieezadeh Abadeh

    (Carnegie Mellon University - David A. Tepper School of Business)

  • Damir Filipović

    (Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute)

  • Daniel Kuhn

    (École polytechnique fédérale de Lausanne)

Abstract

We introduce a universal framework for mean-covariance robust risk measurement and portfolio optimization.We model uncertainty in terms of the Gelbrich distance on the mean-covariance space, along with prior structural information about the population distribution. Our approach is related to the theory of optimal transport and exhibits superior statistical and computational properties than existing models. We find that, for a large class of risk measures, mean-covariance robust portfolio optimization boils down to the Markowitz model, subject to a regularization term given in closed form. This includes the finance standards, value-at-risk and conditional value-at-risk, and can be solved highly efficiently.

Suggested Citation

  • Viet-Anh Nguyen & Soroosh Shafieezadeh Abadeh & Damir Filipović & Daniel Kuhn, 2021. "Mean-Covariance Robust Risk Measurement," Swiss Finance Institute Research Paper Series 21-93, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp2193
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    Keywords

    Robust optimization; risk measurement; optimal transport;
    All these keywords.

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