  This paper extends the classical consumption and portfolio rules model in
continuous time (Merton 1969, 1971) to the framework of decision-makers with
time-inconsistent preferences. The model is solved for different utility
functions for both, naive and sophisticated agents, and the results are
compared. In order to solve the problem for sophisticated agents, we derive a
modified HJB (Hamilton-Jacobi-Bellman) equation. It is illustrated how for CRRA
functions within the family of HARA functions (logarithmic and potential cases)
the optimal portfolio rule does not depend on the discount rate, but this is
not the case for a general utility function, such as the exponential (CARA)
utility function.
