Maximization of the portfolio growth rate under fixed and proportional transaction costs

This paper considers a discrete-time Markovian model of asset prices with economic factors and transaction costs with proportional and fixed terms. Existence of optimal strategies maximizing average growth rate of portfolio is proved in the case of complete and partial observation of the process modeling the economic factors. The proof is based on a modification of the vanishing discount approach. The main difficulty is the discontinuity of the controlled transition operator of the underlying Markov process.