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A multi-period portfolio selection optimization model by using interval analysis

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  • Liu, Yong-Jun
  • Zhang, Wei-Guo
  • Zhang, Pu

Abstract

Due to few historical data that can be obtained in an emerging securities market, the future returns, risk and liquidity of securities cannot be forecasted precisely. The investment environment is usually fuzzy and uncertain. To handle these imprecise data, this paper discusses a fuzzy multi-period portfolio optimization problem where the returns, risk, and liquidity of securities are represented by interval variables. By taking the return, risk, liquidity and diversification degree of portfolio into consideration, an interval multi-period portfolio selection optimization model is proposed with the objective of maximizing the terminal wealth under the constraints of the return, risk and diversification degree of portfolio at each period. In the proposed model, a proportion entropy is employed to measure the diversification degree of portfolio. Using the fuzzy decision-making theory and multi-objective programming approach, the proposed model is transformed into a crisp nonlinear programming. Then, we design an improved particle swarm optimization algorithm for solution. Finally, a numerical example is given to illustrate the application of our model and demonstrate the effectiveness of the designed algorithm.

Suggested Citation

  • Liu, Yong-Jun & Zhang, Wei-Guo & Zhang, Pu, 2013. "A multi-period portfolio selection optimization model by using interval analysis," Economic Modelling, Elsevier, vol. 33(C), pages 113-119.
    • Handle: RePEc:eee:ecmode:v:33:y:2013:i:c:p:113-119
    DOI: 10.1016/j.econmod.2013.03.006
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    Cited by:

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    2. Yuanyuan Zhang & Xiang Li & Sini Guo, 2018. "Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature," Fuzzy Optimization and Decision Making, Springer, vol. 17(2), pages 125-158, June.
    3. P. Kumar & Jyotirmayee Behera & A. K. Bhurjee, 2022. "Solving mean-VaR portfolio selection model with interval-typed random parameter using interval analysis," OPSEARCH, Springer;Operational Research Society of India, vol. 59(1), pages 41-77, March.
    4. Kamali, Rezvan & Mahmoodi, Safieh & Jahandideh, Mohammad-Taghi, 2019. "Optimization of multi-period portfolio model after fitting best distribution," Finance Research Letters, Elsevier, vol. 30(C), pages 44-50.
    5. Natalie Ramírez Carmona & Oswaldo García Salgado, 2016. "State of the art in portfolio theory: the individual analysis of actions to the multiobjective optimization. Estado del arte en teoría de portafolios: del análisis individual de acciones a la optimiza," Economia Coyuntural,Revista de temas de perspectivas y coyuntura, Instituto de Investigaciones Economicas y Sociales 'Jose Ortiz Mercado' (IIES-JOM), Facultad de Ciencias Economicas, Administrativas y Financieras, Universidad Autonoma Gabriel Rene Moreno, vol. 1(4), pages 101-144.
    6. Yong-Jun Liu & Wei-Guo Zhang & Jun-Bo Wang, 2016. "Multi-period cardinality constrained portfolio selection models with interval coefficients," Annals of Operations Research, Springer, vol. 244(2), pages 545-569, September.
    7. Jianjian Wang & Feng He & Xin Shi, 2019. "Numerical solution of a general interval quadratic programming model for portfolio selection," PLOS ONE, Public Library of Science, vol. 14(3), pages 1-16, March.
    8. Yujia Hu, 2023. "A Heuristic Approach to Forecasting and Selection of a Portfolio with Extra High Dimensions," Mathematics, MDPI, vol. 11(6), pages 1-21, March.
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    10. Zhang Peng & Gong Heshan & Lan Weiting, 2017. "Multi-Period Mean-Absolute Deviation Fuzzy Portfolio Selection Model with Entropy Constraints," Journal of Systems Science and Information, De Gruyter, vol. 4(5), pages 428-443, October.

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