Equilibrium consumption and portfolio decisions with stochastic discount rate and time-varying utility functions

This paper studies a multi-period investment-consumption optimization problem with a stochastic discount rate and a time-varying utility function, which are governed by a Markov-modulated regime switching model. The investment is dynamically reallocated between one risk-free asset and one risky asset. The problem is time inconsistent due to the stochastic discount rate. An analytical equilibrium solution is established by resorting to a game theoretical framework. Numerous sensitivity analyses and numerical examples are provided to demonstrate the effects of the stochastic discount rate and time-varying utility coefficients on the decision-maker's investment-consumption behavior. Our results show that many properties which are satisfied in the classical models do not hold any more due to either the stochastic discount rate or the time-varying utility function.