An exact approach for portfolio selection with transaction costs and rounds

We consider a single-period mean-safety portfolio selection problem with transaction costs and integer constraints on the quantities selected for the securities (rounds). We propose an exact approach based on the partition of the initial problem into two subproblems and the use of a simple local search heuristic to obtain an initial solution. To the best of our knowledge, no optimal algorithms have been proposed in the literature for this problem. The proposed approach is simple, general and easily adaptable to other problems. An extensive experimental analysis based on real data from the main international Stock Exchange Markets is performed. The results show, on average, an impressive improvement with respect to the computational time and space memory required by CPLEX 7.0. We also show that the solution of the first subproblem can be used on its own as an extremely effective heuristic.