Numerical methods for optimal decumulation of a defined contribution pension plan

TL;DR

This paper develops a numerical framework using Fourier methods to solve the optimal decumulation problem in defined contribution pension plans, incorporating leverage and constraints.

Contribution

It introduces a Fourier-based numerical approach for solving the stochastic control problem in pension decumulation, addressing issues like leverage and constraints.

Findings

Fourier method ensures monotonicity to O(δ)

Restricting equity to 50% does not significantly reduce efficiency

Effective minimization of wrap-around error in the numerical scheme

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 $\delta$-monotone Fourier method, which ensures that monotonicity holds to $O(\delta)$. 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.