Master’s Research Paper Presentation • Scientific Computing • A Deep Learning Approach to Probability of Shortfall in Defined Contribution Plan Optimization

Please note: This master’s research paper presentation will take place in DC 2310.

Zeyu Zhang, Master’s candidate
David R. Cheriton School of Computer Science

Supervisors: Professors Yuying Li, Peter Forsyth

This study presents a neural network (NN)-based approach to compute the optimal decumulation strategy for retirees with defined contribution (DC) pension plans. Unlike traditional approaches to expected shortfall problems, we introduce a probability of short- fall (PS) term to quantify the risk of fund depletion, balancing withdrawal amounts with the likelihood that terminal wealth falls below a threshold. We demonstrate that one of the main challenges in solving this problem is the non-differentiability of the indicator function, which introduces difficulties in calculating the derivative using Monte Carlo simulation, limiting the effectiveness of gradient-based optimization.

To overcome this, we propose the sigmoid function as a differentiable approximation to the indicator function. Through extensive numerical experiments, we identify good choices of NN hyper-parameters and validate the approach against partial differential equation (PDE) results as a ground truth. Our findings show that the NN solution consistently produces results closely matching those of the PDE method. Furthermore, robustness testing on synthetic and historical datasets highlights the NN’s reliability and practical applicability. Our results highlight the NN’s ability to offer computationally efficient and highly accurate solutions for optimal decumulation strategies. While the probability of shortfall is more interpretable than the expected shortfall, as it quantifies the probability of shortfall occurrence, it does not capture the magnitude of shortfalls. This trade-off underscores the importance of selecting an appropriate risk measure based on investor preferences.