A Primer on Portfolio Choice with Small Transaction Costs

2016/12/05 by Muhle-Karbe, Johannes, Reppen, Max, Soner, H. Mete
#FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM)

paper · doi:10.48550/arxiv.1612.01302

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.

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