ABSTRACT
In the previous chapters, we saw that, at least when using the AlmgrenChriss framework, the optimal trading curve for almost all execution problems was characterized by a Hamiltonian system. In this chapter, we present several numerical methods to approximate the solution of these Hamiltonian systems. For single-asset portfolios, the method we propose is a very simple and efficient shooting method. For more complex portfolios, we propose several methods, depending on the type of execution cost functions.
