Note on Merton's Optimum Consumption and Portfolio Rules in a Continuous-Time Model. Revised

摘要

In the area of consumption and portfolio problem in continuous time, Merton is the most widely cited paper. It is an important paper because of its many significant contributions. Among these was the provision of explicit solutions for utility functions in the HARA family specified in equation (43) of Merton's paper. These solutions in the form of lengthy formulas were simply stated without any derivation. Perhaps, because of this, some errors went undetected. While some minor errors were corrected in Merton, the purpose of this not is to delineate the subfamily of HARA utility functions for which the explicit solution obtained in Section 6 of Merton's paper are correct and the remaining subfamily for which they are not.