A Consumption-Investment Problem With General Utility Functions

A continuous-time, consumption-investment problem with constant market coeffi-cients on a finite horizon is considered for an agent seeking to maximize expected utility from consumption plus expected utility from terminal wealth. Under short-selling pro-hibition, a dual problem is posed and solved with general utility functions, and the value functions for both problems are proved to be solutions to the corresponding HJB equa-tions. The solution to the dual problem provides information about the existence and nature of the solution to the original problem. We also provide examples.