Stability advances in robust portfolio optimization under parallelepiped uncertainty

  • Güray KaraEmail author
  • Ayşe Özmen
  • Gerhard-Wilhelm Weber
Original Paper


In financial markets with high uncertainties, the trade-off between maximizing expected return and minimizing the risk is one of the main challenges in modeling and decision making. Since investors mostly shape their invested amounts towards certain assets and their risk aversion level according to their returns, scientists and practitioners have done studies on that subject since the beginning of the stock markets’ establishment. In this study, we model a Robust Optimization problem based on data. We found a robust optimal solution to our portfolio optimization problem. This approach includes the use of Robust Conditional Value-at-Risk under Parallelepiped Uncertainty, an evaluation and a numerical finding of the robust optimal portfolio allocation. Then, we trace back our robust linear programming model to the Standard Form of a Linear Programming model; consequently, we solve it by a well-chosen algorithm and software package. Uncertainty in parameters, based on uncertainty in the prices, and a risk-return analysis are crucial parts of this study. A numerical experiment and a comparison (back testing) application are presented, containing real-world data from stock markets as well as a simulation study. Our approach increases the stability of portfolio allocation and reduces the portfolio risk.


Robustness and sensitivity analysis Robust optimization Robust conditional value-at-risk Parallelepiped uncertainty Risk management. 



The authors of this paper would gradually thank to the Editor and to the two anonymous reviewers for their important and insightful comments.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • Güray Kara
    • 1
    • 2
    Email author
  • Ayşe Özmen
    • 3
  • Gerhard-Wilhelm Weber
    • 2
    • 4
  1. 1.Department of Industrial Economics and Technology ManagementNorwegian University of Science and TechnologyTrondheimNorway
  2. 2.Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey
  3. 3.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada
  4. 4.Chair of Marketing and Economic Engineering, Faculty of Engineering ManagementPoznan University of TechnologyPoznanPoland

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