The Optimization of the Mean-Variance Portfolio Selection with Nonsmooth Concave Transaction Costs

Abstract

Transaction cost was an important factor in the financial market. According to the situation of the underdeveloped market, we proposed a mean-variance portfolio selection model with nonsmooth concave transaction costs. This is nonsmooth programming problem. The paper proposed the subsection method and pivoting algorithm to solve it, and proved these algorithms convergent. Finally, according to annual yields of six kinds of securities in eight years, we solved the mean-variance portfolio optimal strategy with nonsmooth concave transaction costs. The example was given to illustrate the efficiency of the algorithms, which offered a new way to solve the problems of nonsmooth programming.