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Using Column Generation to Solve Extensions to the Markowitz Model

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  • Lorenz M. Roebers
  • Aras Selvi
  • Juan C. Vera

Abstract

We introduce a solution scheme for portfolio optimization problems with cardinality constraints. Typical portfolio optimization problems are extensions of the classical Markowitz mean-variance portfolio optimization model. We solve such type of problems using a method similar to column generation. In this scheme, the original problem is restricted to a subset of the assets resulting in a master convex quadratic problem. Then the dual information of the master problem is used in a sub-problem to propose more assets to consider. We also consider other extensions to the Markowitz model to diversify the portfolio selection within the given intervals for active weights.

Suggested Citation

  • Lorenz M. Roebers & Aras Selvi & Juan C. Vera, 2018. "Using Column Generation to Solve Extensions to the Markowitz Model," Papers 1812.00093, arXiv.org, revised Jun 2019.
    • Handle: RePEc:arx:papers:1812.00093
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    References listed on IDEAS

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    6. Martijn Cremers & Antti Petajisto, 2006. "How Active is Your Fund Manager? A New Measure That Predicts Performance," Yale School of Management Working Papers amz2370, Yale School of Management, revised 01 May 2009.
    7. Jang Ho Kim & Woo Chang Kim & Frank J. Fabozzi, 2014. "Recent Developments in Robust Portfolios with a Worst-Case Approach," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 103-121, April.
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