Using Column Generation to Solve Extensions to the Markowitz Model

Lorenz M. Roebers, Aras Selvi and Juan C. Vera

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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.

Date: 2018-11, Revised 2019-06
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