# Cutting plane algorithms for mean-CVaR portfolio optimization with nonconvex transaction costs

*Yuichi Takano* (),
*Keisuke Nanjo* (),
*Noriyoshi Sukegawa* () and
*Shinji Mizuno* ()

*Computational Management Science*, 2015, vol. 12, issue 2, 319-340

**Abstract:**
This paper studies the mean-risk portfolio optimization problem with nonconvex transaction costs. We employ the conditional value-at-risk (CVaR) as a risk measure. There are a number of studies that aim at efficiently solving large-scale CVaR minimization problems. None of these studies, however, take into account nonconvex transaction costs, which are present in practical situations. To make a piecewise linear approximation of the transaction cost function, we utilized special ordered set type two constraints. Moreover, we devised a subgradient-based cutting plane algorithm to handle a large number of scenarios. This cutting plane algorithm needs to solve a mixed integer linear programming problem in each iteration, and this requires a substantial computation time. Thus, we also devised a two-phase cutting plane algorithm that is even more efficient. Numerical experiments demonstrated that our algorithms can attain near-optimal solutions to large-scale problems in a reasonable amount of time. Especially when rebalancing a current portfolio that is close to an optimal one, our algorithms considerably outperform other solution methods. Copyright Springer-Verlag Berlin Heidelberg 2015

**Keywords:** Portfolio optimization; Conditional value-at-risk; Cutting plane algorithm; Transaction costs; Mixed integer linear programming (search for similar items in EconPapers)

**Date:** 2015

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