Stability advances in robust portfolio optimization under parallelepiped uncertainty

• Published in: Central European journal of operations research Vol. 27; no. 1; pp. 241 - 261
• Main Authors: Kara, Güray, Özmen, Ayşe, Weber, Gerhard-Wilhelm
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 07.03.2019; Springer; Springer Nature B.V
• Subjects: Business and Management; Computer simulation; Decision making; Linear programming; Markets; Mathematical models; Mathematical optimization; Methods; Operations research; Operations Research/Decision Theory; Optimization; Original Paper; Parameter uncertainty; Portfolio management; Risk analysis; Robustness (mathematics); Securities markets; Stability; Stock exchanges; Uncertainty; Norway; Robust optimization; Robustness and sensitivity analysis; Risk management; Robust conditional value-at-risk; Parallelepiped uncertainty
• ISSN: 1435-246X; 1613-9178; 1613-9178
• DOI: 10.1007/s10100-017-0508-5

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.