Journal of Systems Science and Complexity

, Volume 31, Issue 3, pp 696–733 | Cite as

A Nonlinear Interval Portfolio Selection Model and Its Application in Banks

  • Dawen Yan
  • Yaxing Hu
  • Kinkeung Lai


In classical Markowitz’s Mean-Variance model, parameters such as the mean and covariance of the underlying assets’ future return are assumed to be known exactly. However, this is not always the case. The parameters often correspond to quantities that fall within a range, or can be known ambiguously at the time when investment decision must be made. In such situations, investors determine returns on investment and risks etc. and make portfolio decisions based on experience and economic wisdom. This paper tries to use the concept of interval numbers in the fuzzy set theory to extend the classical mean-variance portfolio selection model to a mean-downside semi-variance model with consideration of liquidity requirements of a bank. The semi-variance constraint is employed to control the downside risk, filling in the existing interval portfolio optimization model based on the linear semi-absolute deviation to depict the downside risk. Simulation results show that the model behaves robustly for risky assets with highest or lowest mean historical rate of return and the optimal investment proportions have good stability. This suggests that for these kinds of assets the model can reduce the risk of high deviation caused by the deviation in the decision maker’s experience and economic wisdom.


Downside-risk management interval return portfolio selection semi-variance simulation 


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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Faculty of Management and EconomicsDalian University of TechnologyDalianChina
  2. 2.School of Mathematical ScienceDalian University of TechnologyDalianChina
  3. 3.Bank of DalianDalianChina
  4. 4.International Business SchoolShaanxi Normal UniversityXi’anChina
  5. 5.College of ManagementXidian UniversityXi’anChina

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