DC programming and DCA for portfolio optimization with linear and fixed transaction costs

Abstract

In this work, a single-period portfolio selection problem which consists of minimizing the total transaction cost subject to different types of constraints on feasible portfolios was considered. The total transaction cost function is separable and discontinuous. This problem is nonconvex and very hard to solve. First, by using additional binary variables, we transform it into a mixed zero-one program and then investigate a DC (Difference of Convex functions) programming framework for designing solution methods. Two approaches are developed: DCA (DC Algorithm) and a combination of DCA and Branch & Bound technique. Computational experiments are reported to demonstrate high efficiency and computational inexpensiveness of DCA, which provides good approximate global solutions. © 2014 Springer International Publishing Switzerland.