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Review on Reformulation of the Mean-Variance Model with Real-life Trading Restrictions

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  • Feng Li

Abstract

In this paper, we consider a class of portfolio selection problems with cardinality and minimum buy-in threshold constraints in real-life which can be formulated as mixed-integer quadratic programming (MIQP). Two reformulation methods that generate the same tight continuous relaxation of original problem are compared in the context under the branch-and-bound algorithm, one is the Perspective Reformulation and another is the Lift-and-Convexification Reformulation (LCR). Computational results show that the (PC) is more competitive than the (LCR) method in terms of computing time and nodes in MIQP solver CPLEX 12.7, what's more, this outperformance becomes more obvious as the size of instances grows.

Suggested Citation

  • Feng Li, 2018. "Review on Reformulation of the Mean-Variance Model with Real-life Trading Restrictions," Asian Social Science, Canadian Center of Science and Education, vol. 14(1), pages 1-40, January.
  • Handle: RePEc:ibn:assjnl:v:14:y:2018:i:1:p:40
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    References listed on IDEAS

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    1. X. Cui & X. Zheng & S. Zhu & X. Sun, 2013. "Convex relaxations and MIQCQP reformulations for a class of cardinality-constrained portfolio selection problems," Journal of Global Optimization, Springer, vol. 56(4), pages 1409-1423, August.
    2. 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.
    3. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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    More about this item

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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