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

Modem asset pricing theory generally assumes frictionless trading. Under th is assumption, an investor would revise his portfolio holdings at every dat e on which he could trade. However, in models where an investor faces finan cial market frictions such as transactions costs, the portfolio is optimall y rebalanced less frequently. This paper examines the portfolio trading pro blem for an investor who faces transactions costs and short sales constrain ts in a continuous time economy with general specifications of ask and bid prices. Our principal results state that the existence of the optimal tradi ng strategy and solution to the investor problem implies the existence of t wo supermartingales whose ratio is bounded by the ask and bid prices and we can identify supporting prices which, in an economy with no transactions c osts, 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. (C) 2000 Elsevi er Science S.A. All rights reserved.