DMCA
A Hamilton-Jacobi-Bellman approach to optimal trade execution (2009)
| Citations: | 15 - 3 self |
BibTeX
@MISC{Forsyth09ahamilton-jacobi-bellman,
author = {Peter A. Forsyth},
title = {A Hamilton-Jacobi-Bellman approach to optimal trade execution},
year = {2009}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
The optimal trade execution problem is formulated in terms of a mean-variance tradeoff, as seen at the initial time. The mean-variance problem can be embedded in a Linear-Quadratic (LQ) optimal stochastic control problem, A semi-Lagrangian scheme is used to solve the resulting non-linear Hamilton Jacobi Bellman (HJB) PDE. This method is essentially independent of the form for the price impact functions. Provided a strong comparision property holds, we prove that the numerical scheme converges to the viscosity solution of the HJB PDE. Numerical examples are presented in terms of the efficient trading frontier and the trading strategy. The numerical results indicate that in some cases there are many different trading strategies which generate almost identical efficient frontiers.
Keyphrases
hamilton-jacobi-bellman approach optimal trade execution optimal trade execution problem semi-lagrangian scheme initial time non-linear hamilton jacobi bellman numerical example price impact function numerical result trading strategy strong comparision property viscosity solution many different trading strategy optimal stochastic control problem mean-variance problem mean-variance tradeoff hjb pde efficient trading frontier identical efficient frontier numerical scheme converges
