A Diffusion Model for Optimal Portfolio Selection in the Presence of Brokerage Fees

We consider a financial market model with two assets. One has deterministic rate of growth, while the rate of growth of the second asset is governed by a Brownian motion with drift. We can shift money from one asset to another; however, there are losses of money (brokerage fees) involved in shifting money from the risky to the nonrisky asset. We want to maximize the expected rate of growth of funds.

It is proved that an optimal policy keeps the ratio of funds in risky and nonrisky assets within a certain interval with minimal effort.