Dynamic portfolio selection with fixed and/or proportional transaction costs using non-singular stochastic optimal control theory

The dynamic portfolio selection problem with fixed and/or proportional transaction costs is studied. The portfolio consists of a risk-free asset, and a risky asset whose price dynamics is governed by geometric Brownian motion. The objective is to find the amounts invested in the risk-free and risky assets that maximize the expected value of the discounted utility of terminal wealth. The dynamic optimization problem is formulated as a non-singular stochastic optimal control problem. Numerical results are presented for buy and sell/no transaction interfaces, and buy and sell targets, that characterize the optimal policies of a constant relative risk aversion investor.