Set-Valued and Variational Analysis

, Volume 26, Issue 4, pp 733–757 | Cite as

A Review on Ambiguity in Stochastic Portfolio Optimization

  • Georg Ch. PflugEmail author
  • Mathias Pohl
Open Access


In mean-risk portfolio optimization, it is typically assumed that the assets follow a known distribution P 0, which is estimated from observed data. Aiming at an investment strategy which is robust against possible misspecification of P 0, the portfolio selection problem is solved with respect to the worst-case distribution within a Wasserstein-neighborhood of P 0. We review tractable formulations of the portfolio selection problem under model ambiguity, as it is called in the literature. For instance, it is known that high model ambiguity leads to equally-weighted portfolio diversification. However, it often happens that the marginal distributions of the assets can be estimated with high accuracy, whereas the dependence structure between the assets remains ambiguous. This leads to the problem of portfolio selection under dependence uncertainty. We show that in this case portfolio concentration becomes optimal as the uncertainty with respect to the estimated dependence structure increases. Hence, distributionally robust portfolio optimization can have two very distinct implications: Diversification on the one hand and concentration on the other hand.


Stochastic optimization Robustness Portfolio optimization Model uncertainty Dependence uncertainty 

Mathematics Subject Classification (2010)

90C15 91B28 



Open access funding provided by University of Vienna. The authors acknowledge support by the Vienna Science and Technologie Fund (WWTF) through project MA14-008.


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Authors and Affiliations

  1. 1.University of ViennaWienAustria

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