This dissertation studies the problem of dynamically trading between taxable and nontaxable assets in order to maximize the expected utility of terminal wealth.
Some properties of the optimal solution are demonstrated and are applied to simplify the representation, analysis and computation of the optimal policy. In particular, the optimal policy can be simply described by one or two target lines in a two-dimensional state space. Here a target line is a curve that consists of the optimal target points on all trading tracks in a certain direction, and a trading track is a set of states with a common characteristic value. The analytical solution for the optimal policy just prior to the termination is also derived. Besides providing a reference for numerical solutions, it can be used throughout the whole time horizon as a good approximate optimal policy.
Several numerical methods are developed for these problems. One method calculates expectation by solving partial differential equations (PDE), and two methods by applying simulation (using point-estimation and regression, respectively). The PDE-based method has the highest computational efficiency and provides the best solution, while the two simulation-based methods can also provide solutions which have investment performance very close to that of PDE-based method.