This review 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 how to simplify them in the small-cost limit. This allows one 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 more complex models, we present a policy iteration scheme that allows one to numerically compute the solution.


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