A Primer on Portfolio Choice with Small Transaction Costs

TL;DR

This paper introduces asymptotic methods for solving portfolio optimization problems with small transaction costs, providing explicit solutions and numerical schemes for complex models.

Contribution

It presents a systematic approach to derive and simplify dynamic programming equations in the small-cost limit, including explicit solutions and a numerical policy iteration scheme.

Findings

Explicit solutions for models with mean-reverting returns

A numerical policy iteration scheme for complex models

Simplified dynamic programming equations in the small-cost limit

Abstract

This survey is an introduction to asymptotic methods for portfolio-choice problems with small transaction costs. We outline how to derive the corresponding dynamic programming equations and simplify them in the small-cost limit. This allows to obtain explicit solutions in a wide range of settings, which we illustrate for a model with mean-reverting expected returns and proportional transaction costs. For even more complex models, we present a policy iteration scheme that allows to compute the solution numerically.