Machine learning and a Hamilton–Jacobi–Bellman equation for optimal decumulation: a comparison study

Without resorting to dynamic programming, we determine the decumulation strategy for the holder of a defined contribution pension plan. We formulate this as a constrained stochastic optimal control problem. Our approach is based on data-driven neural network optimization. Customized activation functions for the output layers of the neural network are applied, which permits training via standard unconstrained optimization. The optimal solution yields a multiperiod decumulation and asset allocation strategy, useful for a holder of a defined contribution pension plan. The objective function of the optimal control problem is a weighted measure of the expected wealth withdrawn and the expected shortfall, and it directly targets left-tail risk. The stochastic bound constraints enforce a guaranteed minimum withdrawal each year. We show that in terms of numerical results the neural network approach compares favorably with a Hamilton–Jacobi–Bellman partial differential equation computational framework.