Explicit solutions to dynamic portfolio choice problems: A continuous-time detour

Recently, many academic researchers have implemented several numerical procedures to solve a dynamic portfolio choice problem especially in incomplete markets. The subsequent numerical results are sometimes significantly different from one paper to another. Thus, they have all advocated the accuracy of their methods. This paper contributes to the previous accuracy debate by showing how to obtain some accurate numerical results without numerical approximations. We use the dynamic programming approach in continuous-time, and illustrate the framework with one risky and one riskless asset. The framework is flexible enough to cover all the HARA class of utility functions. We derive explicit solutions with a stochastic market price of risk and with a stochastic volatility. 7 countries are considered in numerical illustrations.