Portfolio optimization under transaction costs in the CRR model

Abstract

In the CRR model we introduce a transaction cost structure which covers piecewise proportional, fixed and constant costs. For a general utility function we formulate the problem of maximizing the expected utility of terminal wealth as a Markov control problem. An existence result is given and optimal strategies can be described by solutions of the dynamic programming equation. For logarithmic utility we provide detailed solutions in the one-period case and provide examples for the multi-dimensional case and for complex cost structures. For a combination of fixed and proportional costs a fast multi-period algorithm is introduced.