On optimal portfolio trading strategies for an investor facing transactions costs in a continuous trading market (Q1972345)

This paper uses ``martingale'' methods to characterize the portfolio trading problem when an investor faces transactions costs and short sale constraints in a continuous trading financial market with general specifications of ask and bid prices. One of the results of the paper states 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. The author also gives an explicit representation of the value function for a certain class of utility functions.