Financial Friction and Multiplicative Markov Market Game

TL;DR

This paper analyzes long-term growth-optimal investment strategies in markets with transaction costs, providing explicit solutions and insights into how friction impacts optimal behavior and losses.

Contribution

It offers closed-form solutions for growth-optimal strategies under transaction costs using multiple derivation methods, including invariant measures and control theory.

Findings

Explicit formulas for optimal strategies

Non-analytic dependence on friction parameter

Insights into frictional losses and growth optimization

Abstract

We study long-term growth-optimal strategies on a simple market with linear proportional transaction costs. We show that several problems of this sort can be solved in closed form, and explicit the non-analytic dependance of optimal strategies and expected frictional losses of the friction parameter. We present one derivation in terms of invariant measures of drift-diffusion processes (Fokker- Planck approach), and one derivation using the Hamilton-Jacobi-Bellman equation of optimal control theory. We also show that a significant part of the results can be derived without computation by a kind of dimensional analysis. We comment on the extension of the method to other sources of uncertainty, and discuss what conclusions can be drawn about the growth-optimal criterion as such.