A hybrid combinatorial approach to a two-stage stochastic portfolio optimization model with uncertain asset prices

  • Tianxiang CuiEmail author
  • Ruibin Bai
  • Shusheng Ding
  • Andrew J. Parkes
  • Rong Qu
  • Fang He
  • Jingpeng Li


Portfolio optimization is one of the most important problems in the finance field. The traditional Markowitz mean-variance model is often unrealistic since it relies on the perfect market information. In this work, we propose a two-stage stochastic portfolio optimization model with a comprehensive set of real-world trading constraints to address this issue. Our model incorporates the market uncertainty in terms of future asset price scenarios based on asset return distributions stemming from the real market data. Compared with existing models, our model is more reliable since it encompasses real-world trading constraints and it adopts CVaR as the risk measure. Furthermore, our model is more practical because it could help investors to design their future investment strategies based on their future asset price expectations. In order to solve the proposed stochastic model, we develop a hybrid combinatorial approach, which integrates a hybrid algorithm and a linear programming (LP) solver for the problem with a large number of scenarios. The comparison of the computational results obtained with three different metaheuristic algorithms and with our hybrid approach shows the effectiveness of the latter. The superiority of our model is mainly embedded in solution quality. The results demonstrate that our model is capable of solving complex portfolio optimization problems with tremendous scenarios while maintaining high solution quality in a reasonable amount of time and it has outstanding practical investment implications, such as effective portfolio constructions.


Hybrid algorithm Combinatorial approach Stochastic programming Population-based incremental learning Local search Learning inheritance Portfolio optimization problem 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Authors and Affiliations

  • Tianxiang Cui
    • 1
    Email author
  • Ruibin Bai
    • 1
  • Shusheng Ding
    • 2
  • Andrew J. Parkes
    • 3
  • Rong Qu
    • 3
  • Fang He
    • 4
  • Jingpeng Li
    • 5
  1. 1.School of Computer ScienceThe University of Nottingham Ningbo ChinaNingboChina
  2. 2.School of Business and Research Academy of Belt & RoadNingbo UniversityNingboChina
  3. 3.School of Computer ScienceThe University of NottinghamNottinghamUK
  4. 4.Department of Computer Science, Faculty of Science and TechnologyUniversity of WestminsterLondonUK
  5. 5.Division of Computing Science and MathematicsUniversity of StirlingStirlingUK

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