Optimal Decumulation for Retirees using Tontines: a Dynamic Neural Network Based Approach

Abstract

We introduce a new approach for optimizing neural networks (NN) using data to solve a stochastic control problem with stochastic constraints. We utilize customized activation functions for the output layers of the NN, enabling training through standard unconstrained optimization techniques. The resulting optimal solution provides a strategy for allocating and withdrawing assets over multiple periods for an individual with a defined contribution (DC) pension plan. The objective function of the control problem focuses on minimizing left-tail risk by considering expected withdrawals (EW) and expected shortfall (ES). Stochastic bound constraints ensure a minimum yearly withdrawal. By comparing our data-driven approach with the numerical results obtained from a computational framework based on the Hamilton-Jacobi-Bellman (HJB) Partial Differential Equation (PDE), we demonstrate that our method is capable of learning a solution that is close to optimal. We show that the proposed framework is capable of incorporating additional stochastic processes, particularly in cases related to the use of tontines. We illustrate the benefits of using tontines for the decumulation problem and quantify the decrease in risk they bring. We also extend the framework to use more assets and provide test results to show the robustness of the control.