Portfolio selection with regime-switching and state-dependent preferences

In this paper, we consider the consumption–investment problem in a regime-switching model with both the discount function and relative/absolute risk aversion depending on the exogenous environment. We obtain the solutions to this time-inconsistent optimal control problem for both the sophisticated agent and the naive agent for different utilities. We also give some comparisons between the strategies for these two kinds of agents. Our results show that at any time, given the same wealth, the naive agent with power (resp. exponential) utility consumes less (resp. more) than her/his sophisticated counterpart in general, and the sophisticated agent is more sensitive to the change of the exogenous environment.