Log-optimal investment in the long run with proportional transaction costs when using shadow prices

Abstract

We consider a non-consuming agent interested in the maximization of the long-run growth rate of a wealth process investing either in a money market and in one risky asset following a geometric Brownian motion or in futures following an arithmetic Brownian motion. The agent faces proportional transaction costs, and we show how the log-optimal optimal policies in the long run can be derived when using the technical tool of shadow prices.

Keywords

• proportional transaction costs
• logarithmic utility
• shadow prices