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A New and Efficient Algorithm for a Class of Portfolio Selection Problems

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  • Jong-Shi Pang

    (Carnegie-Mellon University, Pittsburgh, Pennsylvania)

Abstract

This paper proposes a new approach and develops an efficient algorithm for solving a class of (simplified) portfolio selection problems. The approach is based on the technique of parametric principal pivoting. The algorithm is particularly suited for problems with special structure and can handle potentially large problems. When specialized to the multiple index model, the algorithm achieves enormous savings in computer storage and computations.

Suggested Citation

  • Jong-Shi Pang, 1980. "A New and Efficient Algorithm for a Class of Portfolio Selection Problems," Operations Research, INFORMS, vol. 28(3-part-ii), pages 754-767, June.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:3-part-ii:p:754-767
    DOI: 10.1287/opre.28.3.754
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    Cited by:

    1. Patriksson, Michael, 2008. "A survey on the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 185(1), pages 1-46, February.
    2. Zhang, Wei-Guo & Wang, Ying-Luo, 2008. "An analytic derivation of admissible efficient frontier with borrowing," European Journal of Operational Research, Elsevier, vol. 184(1), pages 229-243, January.
    3. Zhang, Xili & Zhang, Weiguo & Xiao, Weilin, 2013. "Multi-period portfolio optimization under possibility measures," Economic Modelling, Elsevier, vol. 35(C), pages 401-408.
    4. Li, Ting & Zhang, Weiguo & Xu, Weijun, 2013. "Fuzzy possibilistic portfolio selection model with VaR constraint and risk-free investment," Economic Modelling, Elsevier, vol. 31(C), pages 12-17.
    5. Bretthauer, Kurt M. & Shetty, Bala, 2002. "The nonlinear knapsack problem - algorithms and applications," European Journal of Operational Research, Elsevier, vol. 138(3), pages 459-472, May.
    6. Immanuel Bomze & Chen Ling & Liqun Qi & Xinzhen Zhang, 2012. "Standard bi-quadratic optimization problems and unconstrained polynomial reformulations," Journal of Global Optimization, Springer, vol. 52(4), pages 663-687, April.
    7. Kuen-Suan Chen & Yin-Yin Huang & Ruey-Chyn Tsaur & Nei-Yu Lin, 2023. "Fuzzy Portfolio Selection in the Risk Attitudes of Dimension Analysis under the Adjustable Security Proportions," Mathematics, MDPI, vol. 11(5), pages 1-16, February.
    8. Zhang, Wei-Guo & Xiao, Wei-Lin & Xu, Wei-Jun, 2010. "A possibilistic portfolio adjusting model with new added assets," Economic Modelling, Elsevier, vol. 27(1), pages 208-213, January.
    9. Torrealba, E.M.R. & Silva, J.G. & Matioli, L.C. & Kolossoski, O. & Santos, P.S.M., 2022. "Augmented Lagrangian algorithms for solving the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 299(1), pages 46-59.
    10. Zhang, Wei-Guo & Zhang, Xi-Li & Xiao, Wei-Lin, 2009. "Portfolio selection under possibilistic mean-variance utility and a SMO algorithm," European Journal of Operational Research, Elsevier, vol. 197(2), pages 693-700, September.
    11. Yin-Yin Huang & Ruey-Chyn Tsaur & Nei-Chin Huang, 2022. "Sustainable Fuzzy Portfolio Selection Concerning Multi-Objective Risk Attitudes in Group Decision," Mathematics, MDPI, vol. 10(18), pages 1-15, September.
    12. Tsaur, Ruey-Chyn, 2013. "Fuzzy portfolio model with different investor risk attitudes," European Journal of Operational Research, Elsevier, vol. 227(2), pages 385-390.
    13. Kuen-Suan Chen & Ruey-Chyn Tsaur & Nei-Chih Lin, 2022. "Dimensions Analysis to Excess Investment in Fuzzy Portfolio Model from the Threshold of Guaranteed Return Rates," Mathematics, MDPI, vol. 11(1), pages 1-13, December.
    14. Syam, Siddhartha S., 1998. "A dual ascent method for the portfolio selection problem with multiple constraints and linked proposals," European Journal of Operational Research, Elsevier, vol. 108(1), pages 196-207, July.
    15. Ruey-Chyn Tsaur, 2015. "Fuzzy portfolio model with fuzzy-input return rates and fuzzy-output proportions," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(3), pages 438-450, February.
    16. White, D.J., 1998. "Epsilon-dominating solutions in mean-variance portfolio analysis," European Journal of Operational Research, Elsevier, vol. 105(3), pages 457-466, March.
    17. Chen, Wei & Zhang, Wei-Guo, 2010. "The admissible portfolio selection problem with transaction costs and an improved PSO algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(10), pages 2070-2076.
    18. Li, Ting & Zhang, Weiguo & Xu, Weijun, 2015. "A fuzzy portfolio selection model with background risk," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 505-513.
    19. Ruey-Chyn Tsaur & Chien-Liang Chiu & Yin-Yin Huang, 2021. "Fuzzy Portfolio Selection in COVID-19 Spreading Period Using Fuzzy Goal Programming Model," Mathematics, MDPI, vol. 9(8), pages 1-15, April.

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