A Primer on Portfolio Choice with Small Transaction Costs
  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. 
Johannes Muhle-Karbe and Max Reppen and H. Mete Soner
q-fin.PM math.OC