On optimal portfolio trading strategies for an investor facing transactions costs in a continuous trading market

Modern asset pricing theory generally assumes frictionless trading. Under this assumption, an investor would revise his portfolio holdings at every date on which he could trade. However, in models where an investor faces financial market frictions such as transactions costs, the portfolio is optimally rebalanced less frequently. This paper examines the portfolio trading problem for an investor who faces transactions costs and short sales constraints in a continuous time economy with general specifications of ask and bid prices. Our principal results state that the existence of the optimal trading strategy and solution to the investor problem implies the existence of two supermartingales whose ratio is bounded by the ask and bid prices and we can identify supporting prices which, in an economy with no transactions costs, would yield the trading strategy and optimal solution of the original economy. This leads to explicit representations of the value function for utility functions commonly analyzed in financial economics. q 2000 Elsevier Science S.A. All rights reserved.