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

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  • Peter A. Forsyth

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.

Suggested Citation

  • Peter A. Forsyth, 2022. "A Stochastic Control Approach to Defined Contribution Plan Decumulation: “The Nastiest, Hardest Problem in Finance”," North American Actuarial Journal, Taylor & Francis Journals, vol. 26(2), pages 227-251, April.
    • Handle: RePEc:taf:uaajxx:v:26:y:2022:i:2:p:227-251
    DOI: 10.1080/10920277.2021.1878043
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    Cited by:

    1. Pieter M. van Staden & Peter A. Forsyth & Yuying Li, 2023. "A parsimonious neural network approach to solve portfolio optimization problems without using dynamic programming," Papers 2303.08968, arXiv.org.
    2. Marc Chen & Mohammad Shirazi & Peter A. Forsyth & Yuying Li, 2023. "Machine Learning and Hamilton-Jacobi-Bellman Equation for Optimal Decumulation: a Comparison Study," Papers 2306.10582, arXiv.org.
    3. Peter A. Forsyth & Kenneth R. Vetzal & G. Westmacott, 2022. "Optimal performance of a tontine overlay subject to withdrawal constraints," Papers 2211.10509, arXiv.org.

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