An Optimal Decision Approach of Post-retirement Investment using Dynamic Programming

Post-retirement investment decision making and as-set allocation have often relied on the Merton’s portfolio problem to model to dictate consumption. While this model excels in being easy to analyze and generalize and has a closed form solution, it omits concrete and accurate criteria to assess the utility of a withdrawal. This research presents a novel utility function for assessing withdrawal efficiency, based on the framework of the consistency principle. This principle proposes that maximum utility is achieved when the withdrawal amount is constant at target percentage α through the planning horizon. The problem is formulated as an optimal control problem and is solved using dynamic programming. A simulation study confirms the model’s accuracy by simulating 10,000 random walks. While the model uses sample data from SPY and TLT ETFs, the model is versatile to incorporate exogenously provided portfolios. It also factors in longevity risk with minor modification. The paper proposes future avenues of exploration to expand the number of variables and use reinforcement learning as a method to resolve significantly more complex problems.