SINGULAR PERTURBATION EXPANSION FOR UTILITY MAXIMIZATION WITH ORDER-ε QUADRATIC TRANSACTION COSTS

We present an expansion for portfolio optimization in the presence of small, instantaneous, quadratic transaction costs. Specifically, the magnitude of transaction costs has a coefficient that is of the order epsilon small, which leads to the optimization problem having an asymptotically-singular Hamilton-Jacobi-Bellman equation whose solution can be expanded in powers of root epsilon. In this paper, we derive explicit formulae for the first two terms of this expansion. Analysis and simulation are provided to show the behavior of this approximating solution.