Almost log-optimal trading strategies for small transaction costs in model with stochastic coefficients

Abstract

We consider a non-consuming agent investing in a stock and a money market interested in the portfolio market price far in the future. We derive a strategy which is almost log-optimal in the long run in the presence of small proportional transaction costs for the case when the rate of return and the volatility of the stock market price are bounded Itô processes with bounded coefficients and when the volatility is bounded away from zero.