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Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints


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  • N. J. Jobst
  • M. D. Horniman
  • C. A. Lucas
  • G. Mitra
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    We consider the mean-variance (M-V) model of Markowitz and the construction of the risk-return efficient frontier. We examine the effects of applying buy-in thresholds, cardinality constraints and transaction roundlot restrictions to the portfolio selection problem. Such discrete constraints are of practical importance but make the efficient frontier discontinuous. The resulting quadratic mixed-integer (QMIP) problems are NP-hard and therefore computing the entire efficient frontier is computationally challenging. We propose alternative approaches for computing this frontier and provide insight into its discontinuous structure. Computational results are reported for a set of benchmark test problems.

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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

    Volume (Year): 1 (2001)
    Issue (Month): 5 ()
    Pages: 489-501

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    Handle: RePEc:taf:quantf:v:1:y:2001:i:5:p:489-501

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    Cited by:
    1. Walter Briec & Kristiaan Kerstens & Octave Jokung, 2007. "Mean-Variance-Skewness Portfolio Performance Gauging: A General Shortage Function and Dual Approach," Management Science, INFORMS, vol. 53(1), pages 135-149, January.
    2. Derigs, Ulrich & Marzban, Shehab, 2009. "New strategies and a new paradigm for Shariah-compliant portfolio optimization," Journal of Banking & Finance, Elsevier, vol. 33(6), pages 1166-1176, June.
    3. Mansini, Renata & Ogryczak, Wlodzimierz & Speranza, M. Grazia, 2014. "Twenty years of linear programming based portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 518-535.
    4. Enrico Angelelli & Renata Mansini & M. Speranza, 2012. "Kernel Search: a new heuristic framework for portfolio selection," Computational Optimization and Applications, Springer, vol. 51(1), pages 345-361, January.
    5. M. Bartholomew-Biggs & S. Kane, 2009. "A global optimization problem in portfolio selection," Computational Management Science, Springer, vol. 6(3), pages 329-345, August.
    6. Konstantinos Anagnostopoulos & Georgios Mamanis, 2011. "Multiobjective evolutionary algorithms for complex portfolio optimization problems," Computational Management Science, Springer, vol. 8(3), pages 259-279, August.
    7. Jobst, Norbert J. & Mitra, Gautam & Zenios, Stavros A., 2006. "Integrating market and credit risk: A simulation and optimisation perspective," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 717-742, February.
    8. Hoai Le Thi & Mahdi Moeini & Tao Pham Dinh, 2009. "Portfolio selection under downside risk measures and cardinality constraints based on DC programming and DCA," Computational Management Science, Springer, vol. 6(4), pages 459-475, October.
    9. Castro, F. & Gago, J. & Hartillo, I. & Puerto, J. & Ucha, J.M., 2011. "An algebraic approach to integer portfolio problems," European Journal of Operational Research, Elsevier, vol. 210(3), pages 647-659, May.
    10. Aouni, Belaid & Colapinto, Cinzia & La Torre, Davide, 2014. "Financial portfolio management through the goal programming model: Current state-of-the-art," European Journal of Operational Research, Elsevier, vol. 234(2), pages 536-545.
    11. Angelelli, Enrico & Mansini, Renata & Speranza, M. Grazia, 2008. "A comparison of MAD and CVaR models with real features," Journal of Banking & Finance, Elsevier, vol. 32(7), pages 1188-1197, July.
    12. Woodside-Oriakhi, M. & Lucas, C. & Beasley, J.E., 2011. "Heuristic algorithms for the cardinality constrained efficient frontier," European Journal of Operational Research, Elsevier, vol. 213(3), pages 538-550, September.
    13. Corazza, Marco & Favaretto, Daniela, 2007. "On the existence of solutions to the quadratic mixed-integer mean-variance portfolio selection problem," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1947-1960, February.
    14. 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.
    15. K.P. Anagnostopoulos & P.D. Chatzoglou & S. Katsavounis, 2010. "A reactive greedy randomized adaptive search procedure for a mixed integer portfolio optimization problem," Managerial Finance, Emerald Group Publishing, vol. 36(12), pages 1057-1065, December.
    16. Wu, Lan & Yang, Yuehan & Liu, Hanzhong, 2014. "Nonnegative-lasso and application in index tracking," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 116-126.
    17. Yucheng Kao & Hsiu-Tzu Cheng, 2013. "Bacterial Foraging Optimization Approach to Portfolio Optimization," Computational Economics, Society for Computational Economics, vol. 42(4), pages 453-470, December.
    18. Briec, Walter & Kerstens, Kristiaan, 2009. "Multi-horizon Markowitz portfolio performance appraisals: A general approach," Omega, Elsevier, vol. 37(1), pages 50-62, February.


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