A DC Programming Framework for Portfolio Selection by Minimizing the Transaction Costs

We consider a single-period portfolio selection problem which consists of minimizing the total transaction cost subject to different types of constraints on feasible portfolios. The transaction cost function is separable, i.e., it is the sum of the transaction cost associated with each trade, but discontinuous. This optimization problem is nonconvex and very hard to solve. We investigate in this work a DC (Difference of Convex functions) programming framework for the solution methods. First, the objective function is approximated by a DC function. Then a DC formulation for the resulting problem is proposed for which two approaches are developed: DCA (DC Algorithm) and a hybridization of Branch and Bound and DCA.