Mean-Covariance Robust Risk Measurement

Viet Anh Nguyen(viet-anh.nguyenstanford.edu)
Soroosh Shafieezadeh-Abadeh(sshafieeandrew.cmu.edu)
Damir Filipovic(damir.filipovicepfl.ch)
Daniel Kuhn(daniel.kuhnepfl.ch)

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.

Keywords: Robust optimization, risk measurement,

Category 1: Robust Optimization

Category 2: Stochastic Programming

Category 3: Applications -- OR and Management Sciences (Finance and Economics )

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Entry Submitted: 12/19/2021
Entry Accepted: 12/20/2021
Entry Last Modified: 12/19/2021

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