Growth optimal policies with transaction costs

In this work, we address the problem of growth optimal investment. This problem was introduced in i.i.d. markets by Breiman [1]. Since then it has been extended to stationary ergodic markets markets and also to markets with no distributional assumptions [2],[3],[4]. The previous work assumes that the market has no transaction costs, i.e. the investor is allowed to trade at no cost. Constant rebalanced strategies that are optimal in the frictionless case would lead to immediate bankruptcy in markets with costs. We extend the growth optimal framework to markets with costs.