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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.

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  • Peter A. Forsyth, 2020. "A Stochastic Control Approach to Defined Contribution Plan Decumulation: "The Nastiest, Hardest Problem in Finance"," Papers 2008.06598, arXiv.org.
    • Handle: RePEc:arx:papers:2008.06598
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    References listed on IDEAS

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    1. Elena Vigna, 2014. "On efficiency of mean--variance based portfolio selection in defined contribution pension schemes," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 237-258, February.
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    4. Menoncin, Francesco & Vigna, Elena, 2017. "Mean–variance target-based optimisation for defined contribution pension schemes in a stochastic framework," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 172-184.
    5. Van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2018. "Time-consistent mean–variance portfolio optimization: A numerical impulse control approach," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 9-28.
    6. Peijnenburg, Kim & Nijman, Theo & Werker, Bas J.M., 2016. "The annuity puzzle remains a puzzle," Journal of Economic Dynamics and Control, Elsevier, vol. 70(C), pages 18-35.
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    9. Cecilia Mancini, 2009. "Non‐parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 270-296, June.
    10. Lin, Yijia & MacMinn, Richard D. & Tian, Ruilin, 2015. "De-risking defined benefit plans," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 52-65.
    11. Peter A. Forsyth & Kenneth R. Vetzal, 2019. "Optimal Asset Allocation for Retirement Saving: Deterministic Vs. Time Consistent Adaptive Strategies," Applied Mathematical Finance, Taylor & Francis Journals, vol. 26(1), pages 1-37, January.
    12. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    13. Forsyth, Peter A. & Vetzal, Kenneth R. & Westmacott, Graham, 2020. "Optimal Asset Allocation For Dc Pension Decumulation With A Variable Spending Rule," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 419-447, May.
    14. Peter A. Forsyth & Kenneth R. Vetzal & Graham Westmacott, 2019. "Management of Portfolio Depletion Risk through Optimal Life Cycle Asset Allocation," North American Actuarial Journal, Taylor & Francis Journals, vol. 23(3), pages 447-468, July.
    15. Dimitris Politis & Halbert White, 2004. "Automatic Block-Length Selection for the Dependent Bootstrap," Econometric Reviews, Taylor & Francis Journals, vol. 23(1), pages 53-70.
    16. Forsyth, Peter A., 2020. "Optimal dynamic asset allocation for DC plan accumulation/decumulation: Ambition-CVAR," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 230-245.
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