Singular Perturbation Expansion for Utility Maximization with Order-ε Quadratic Transaction Costs
Forthcoming, International Journal of Theoretical and Applied Finance
16 Pages Posted: 29 Jun 2017 Last revised: 25 Nov 2019
Date Written: May 13, 2019
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 $\sqrt\epsilon$. 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.
Keywords: Transaction costs; singular perturbation expansion; stochastic control; Merton problem; aim portfolio
JEL Classification: C61; D40
Suggested Citation: Suggested Citation