Multi-period power utility optimization under stock return predictability

In this paper, we derive an analytical solution to the dynamic optimal portfolio choice problem in the case of an investor equipped with a power utility function of wealth. The results are established by solving the Bellman backward recursion under the assumption that the vector of asset returns follows a vector-autoregressive process with predictable variables. In an empirical study, the performance of the derived solution is compared with the one obtained by applying the numerical method. The comparison is performed in terms of the final wealth and its expected utility. It is documented that the application of the analytical solution to the multi-period portfolio choice problem leads to higher values of both the final wealth and the expected utility.