Throughout the world, Defined Benefit (DB) pension plans are disappearing: governments and corporations no longer want to assume the risk. Defined Contribution (DC) pension plans are becoming the norm. When a DC plan holder retires, the retiree must decide on (i) an asset allocation and (ii) awithdrawal strategy. This has been termed "the nastiest, hardest problem in finance" by William Sharpe.

We pose the DC decumulation problem as an optimal stochastic control with a finite investment horizon.The controls are the annual withdrawals and the investment allocations. The reward is the total amount withdrawn, while the risk is measured as the expected shortfall at the end of the investment horizon. We constrain the withdrawals (maximum and minimum amounts) as well as impose no-shorting and no-leverage on the asset allocations.

Traditionally, computing such optimal controls is based on dynamic programming (DP), e.g., PDE or reinforcement learning. Using DP, computing a value function at each rebalancing time requires maximizing a conditional expectation. We propose a neural network (NN) Policy Function Approximation (PFA) method which learns the optimal dynamic policies, without using DP, directly from data. While DP requires computing a high dimensional conditional expectation, our proposed approach achieves efficiency by solving a low dimensional control directly based on a single optimization problem.

We compare this method to ground truth results computed by solving (numerically) a Hamilton Jacobi-Bellman PDE. Our NN-PFA method has the advantage of straightforward application to high-dimensional problems, and can also be used in pure data-driven mode, which does not require specification of a parametric model for asset returns.

Bio: Yuying Li is a professor at the Cheriton School of Computer Science at the University of Waterloo in Canada. Prior to joining UW, she was a senior research associate at Cornell University 1988-2005. She is also the recipient of the 1993 Leslie Fox first Prize in numerical analysis competition held at Oxford England. Her research interests include financial data science, machine learning, computational finance, and computational optimization. Li is currently an associate editor for Journal of Computational Finance, as well as Journal of Finance and Data Science.