Mean–variance portfolio optimal problem under concave transaction cost

In this paper, the classical mean–variance portfolio model is modified for calculating a globally optimal portfolio under concave transaction costs. A non-decreasing concave function is employed to approximate origin transaction cost function. The resulting model is a D-C (difference of two convex functions) programming and a branch and bound algorithm is designed to solve the problem. A series of numerical experiments on the model is presented. The history data of nine stocks in Shan Xi province is used in experiments, and efficient frontiers generated from the resulting model with different limitations on investments are presented to show the effect of the model and the efficiency of the algorithm solving the model.