Numerical methods for optimal decumulation of a defined contribution pension plan

2026-05-17

AI Summary

This study addresses the optimal asset allocation problem during the decumulation phase of defined-contribution pension plans, which constitutes a high-dimensional stochastic control challenge. We formulate the withdrawal strategy as a stochastic dynamic programming problem and iteratively solve, at each rebalancing step, a linear partial integro-differential equation (PIDE) coupled with an optimization subproblem. To efficiently solve the PIDE, we innovatively employ a δ-monotone Fourier method that effectively mitigates wrap-around errors. Combined with numerical optimization techniques, our approach accommodates realistic constraints such as leverage usage and minimum bond holdings. Numerical results demonstrate that capping equity exposure at 50% has negligible impact on portfolio efficiency while substantially reducing risk, thereby offering risk-averse retirees a robust and practical decumulation strategy.

Abstract

The decumulation of a defined contribution (DC) pension plan is well known to be one of the hardest problems in finance. We model this decumulation challenge as an optimal stochastic control problem. The control problem is solved, at each rebalancing date, by alternatively solving a linear partial-integro differential equation (PIDE) followed by an optimization step. We solve the PIDE by using a $δ$-monotone Fourier method, which ensures that monotonicity holds to $O(δ)$. We allow for the use of leverage (i.e. borrowing to invest in stocks), as well as minimum constraints on bond holdings. We pay particular attention to minimizing wrap-around error, an issue which is endemic for Fourier methods and central to the effective use of these methods for optimal control problems. Rather unexpectedly, we find that restricting the portfolio equity fraction to a maximum of 50\% does not reduce portfolio efficiency noticeably. This may be a useful strategy for risk-averse retirees.

Problem

• defined contribution pension
• optimal decumulation
• stochastic control
• portfolio allocation
• retirement risk

Innovation

• δ-monotone Fourier method
• optimal stochastic control
• partial-integro differential equation (PIDE)
• wrap-around error
• defined contribution pension decumulation