Optimal portfolio selection with both fixed and proportional transaction costs for a CRRA investor with finite horizon

This revision: January 22, 2002In this paper we study the optimal portfolio selection problem for a constant relative risk averse investor who faces fixed and proportional transaction costs and maximizes expected utility of end-of-period wealth. We use a continuous time model and apply the method of the Markov chain approximation to solve numerically for the optimal trading policy. The numerical solution indicates that the portfolio space is divided into three disjoint regions (Buy, Sell, and No-Transaction), and four boundaries describe the optimal policy. If a portfolio lies in the Buy region, the optimal strategy is to buy the risky asset until the portfolio reaches the lower (Buy) target boundary. Similarly, if a portfolio lies in the Sell region, the optimal strategy is to sell the risky asset until the portfolio reaches the upper (Sell) target boundary. All these boundaries are functions of the investor's horizon and the composition of the investor's wealth. Some important properties of the optimal policy are as follows: As the terminal date approaches, the NT region widens. And the NT region widens as wealth declines. As the investor's wealth increases the target boundaries converge quickly to the NT boundaries in the corresponding model with proportional transaction costs only. As wealth becomes small, the target boundaries move closer to the Merton line. The closer the terminal date, the earlier this movement begins. The effects on the optimal policy from varying volatility, drift, CRRA, and the level of transaction costs are also examined