Growth-optimal portfolios under transaction costs

TL;DR

This paper develops a model for optimal portfolio growth considering transaction costs, demonstrating the existence of a Markovian strategy that maximizes long-term growth rate using advanced probabilistic methods.

Contribution

It introduces a novel approach to portfolio optimization with transaction costs, proving the existence of a Markovian optimal strategy in a Markovian market model.

Findings

Existence of a growth-optimal, Markovian trading strategy.

Application of large deviations estimates to portfolio optimization.

Extension of vanishing discount method to discontinuous operators.

Abstract

This paper studies a portfolio optimization problem in a discrete-time Markovian model of a financial market, in which asset price dynamics depend on an external process of economic factors. There are transaction costs with a structure that covers, in particular, the case of fixed plus proportional costs. We prove that there exists a self-financing trading strategy maximizing the average growth rate of the portfolio wealth. We show that this strategy has a Markovian form. Our result is obtained by large deviations estimates on empirical measures of the price process and by a generalization of the vanishing discount method to discontinuous transition operators.