A Stochastic Control Approach to Defined Contribution Plan Decumulation: "The Nastiest, Hardest Problem in Finance"

TL;DR

This paper formulates the decumulation phase of a Defined Contribution pension as an optimal stochastic control problem, optimizing withdrawals and asset allocation to maximize expected withdrawals while managing risk.

Contribution

It introduces a novel stochastic control framework for DC plan decumulation, incorporating constraints and risk measures, and demonstrates its robustness through numerical solutions and historical data testing.

Findings

Optimal strategies increase expected withdrawals with minimal risk increase.

Numerical solutions effectively handle constraints and risk measures.

Robustness confirmed via historical data resampling.

Abstract

We pose the decumulation strategy for a Defined Contribution (DC) pension plan as a problem in optimal stochastic control. The controls are the withdrawal amounts and the asset allocation strategy. We impose maximum and minimum constraints on the withdrawal amounts, and impose no-shorting no-leverage constraints on the asset allocation strategy. Our objective function measures reward as the expected total withdrawals over the decumulation horizon, and risk is measured by Expected Shortfall (ES) at the end of the decumulation period. We solve the stochastic control problem numerically, based on a parametric model of market stochastic processes. We find that, compared to a fixed constant withdrawal strategy, with minimum withdrawal set to the constant withdrawal amount, the optimal strategy has a significantly higher expected average withdrawal, at the cost of a very small increase in ES risk. Tests on bootstrapped resampled historical market data indicate that this strategy is robust to parametric model misspecification.