Growth optimal portfolios in discrete-time markets under transaction costs

Abstract

We investigate portfolio selection problem from a signal processing perspective and study how and when an investor should diversify wealth over two assets in order to maximize the cumulative wealth. We construct portfolios that provide the optimal growth in i.i.d. discrete time two-asset markets under proportional transaction costs. As the market model, we consider arbitrary discrete distributions on the price relative vectors, which can also be used to approximate a wide class of continuous distributions. To achieve optimal growth, we use threshold portfolios, where we introduce an iterative algorithm to calculate the expected wealth. Subsequently, the corresponding parameters are optimized using a brute force approach yielding the growth optimal portfolio under proportional transaction costs in i.i.d. discrete-time two-asset markets.