Multi-period mean-variance portfolio selection with fixed and proportional transaction costs

Portfolio selection problem is one of the core research fields in modern financial economics. Considering the transaction costs in multi-period investments makes portfolio selection problems hard to solve. In this paper, the multi-period mean-variance portfolio selection problems with fixed and proportional transaction costs are investigated. By introducing the Lagrange multiplier and using the dynamic programming approach, the indirect utility function is defined for solving the portfolio selection problem constructed in this paper. The optimal strategies and the boundaries of the no-transaction region are obtained in the explicit form. And the efficient frontier for the original portfolio selection problems is also given. Numerical result shows that the method provided in this paper works well.