A Dynamic Programming Approach to Subsistence Consumption Constraints on Optimal Consumption and Portfolio

We investigate an optimal consumption and portfolio selection problem of an infinitely-lived economic agent with a constant relative risk aversion (CRRA) utility function who faces subsistence consumption constraints. We provide the closed form solutions for the optimal consumption and investment policies by using the dynamic programming method and compare the solutions with those obtained by the martingale method. We show that they coincide with each other. Comparison of optimal policies with and without subsistence consumption constraints shows that the constraints have effect on the optimal consumption and portfolio policies even when the constraints do not bind.