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Quadratic programming for portfolio planning: Insights into algorithmic and computational issues Part II — Processing of portfolio planning models with discrete constraints

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  • Gautam Mitra

    (CARISMA — The Centre for the Analysis of Risk Optimisation Modelling Applications, Brunel University)

  • Frank Ellison
  • Alan Scowcroft

Abstract

Convex quadratic programming as applied to portfolio planning is established and well understood. In this paper, presented in two parts, we highlight the importance of choosing an algorithm that processes a family of problems efficiently. In Part I (published in issue 8/3), in particular, we described an adaptation of the simplex method for Quadratic Programming (QP). The method not only takes advantage of the sparse features of simplex, the use of the duality property makes it ideally suited for processing the discrete optimisation models. Part II of the paper considers a family of discrete QP formulations of the portfolio problem, which capture threshold constraints and cardinality restrictions. We describe the adaptation a novel method ‘branch, fix and relax’ to process this class of models efficiently. Theory and computational results are presented.

Suggested Citation

  • Gautam Mitra & Frank Ellison & Alan Scowcroft, 2007. "Quadratic programming for portfolio planning: Insights into algorithmic and computational issues Part II — Processing of portfolio planning models with discrete constraints," Journal of Asset Management, Palgrave Macmillan, vol. 8(4), pages 249-258, November.
    • Handle: RePEc:pal:assmgt:v:8:y:2007:i:4:d:10.1057_palgrave.jam.2250079
    DOI: 10.1057/palgrave.jam.2250079
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    References listed on IDEAS

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    1. E. L. Lawler & D. E. Wood, 1966. "Branch-and-Bound Methods: A Survey," Operations Research, INFORMS, vol. 14(4), pages 699-719, August.
    2. N. J. Jobst & M. D. Horniman & C. A. Lucas & G. Mitra, 2001. "Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 489-501.
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    Cited by:

    1. P. Bonami & M. A. Lejeune, 2009. "An Exact Solution Approach for Portfolio Optimization Problems Under Stochastic and Integer Constraints," Operations Research, INFORMS, vol. 57(3), pages 650-670, June.
    2. Panos Xidonas & Christis Hassapis & George Mavrotas & Christos Staikouras & Constantin Zopounidis, 2018. "Multiobjective portfolio optimization: bridging mathematical theory with asset management practice," Annals of Operations Research, Springer, vol. 267(1), pages 585-606, August.
    3. Khodamoradi, T. & Salahi, M. & Najafi, A.R., 2020. "Robust CCMV model with short selling and risk-neutral interest rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    4. Xiaojin Zheng & Xiaoling Sun & Duan Li, 2014. "Improving the Performance of MIQP Solvers for Quadratic Programs with Cardinality and Minimum Threshold Constraints: A Semidefinite Program Approach," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 690-703, November.

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