Dynamic Mean-Variance Portfolio Selection with Transaction Costs

Abstract

This paper investigates a mean-variance portfolio selection problem in continuous time with fixed and proportional transaction costs. Utilizing the dynamic programming, the Hamilton-Jacobi-Bellman (HJB) equation is derived, and the explicit closed form solution is obtained. Furthermore, the optimal strategies and efficient frontiers are also proposed for the original mean-variance problem. Numerical experiments present the variation of the transaction region and efficient frontier with the transaction costs change, which demonstrate the proposed method performs effective.