IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2306.10582.html
   My bibliography  Save this paper

Machine Learning and Hamilton-Jacobi-Bellman Equation for Optimal Decumulation: a Comparison Study

Author

Listed:
  • Marc Chen
  • Mohammad Shirazi
  • Peter A. Forsyth
  • Yuying Li

Abstract

We propose a novel data-driven neural network (NN) optimization framework for solving an optimal stochastic control problem under stochastic constraints. Customized activation functions for the output layers of the NN are applied, which permits training via standard unconstrained optimization. The optimal solution yields a multi-period asset allocation and decumulation strategy for a holder of a defined contribution (DC) pension plan. The objective function of the optimal control problem is based on expected wealth withdrawn (EW) and expected shortfall (ES) that directly targets left-tail risk. The stochastic bound constraints enforce a guaranteed minimum withdrawal each year. We demonstrate that the data-driven approach is capable of learning a near-optimal solution by benchmarking it against the numerical results from a Hamilton-Jacobi-Bellman (HJB) Partial Differential Equation (PDE) computational framework.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2306.10582
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2306.10582
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Lin, Yijia & MacMinn, Richard D. & Tian, Ruilin, 2015. "De-risking defined benefit plans," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 52-65.
    3. repec:imf:imfdps:2021/024 is not listed on IDEAS
    4. Anarkulova, Aizhan & Cederburg, Scott & O’Doherty, Michael S., 2022. "Stocks for the long run? Evidence from a broad sample of developed markets," Journal of Financial Economics, Elsevier, vol. 143(1), pages 409-433.
    5. 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.
    6. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    7. Dang, D.M. & Forsyth, P.A., 2016. "Better than pre-commitment mean-variance portfolio allocation strategies: A semi-self-financing Hamilton–Jacobi–Bellman equation approach," European Journal of Operational Research, Elsevier, vol. 250(3), pages 827-841.
    8. Hubert Dichtl & Wolfgang Drobetz & Martin Wambach, 2016. "Testing rebalancing strategies for stock-bond portfolios across different asset allocations," Applied Economics, Taylor & Francis Journals, vol. 48(9), pages 772-788, February.
    9. Tomas Björk & Agatha Murgoci, 2014. "A theory of Markovian time-inconsistent stochastic control in discrete time," Finance and Stochastics, Springer, vol. 18(3), pages 545-592, July.
    10. Andrew Patton & Dimitris Politis & Halbert White, 2009. "Correction to “Automatic Block-Length Selection for the Dependent Bootstrap” by D. Politis and H. White," Econometric Reviews, Taylor & Francis Journals, vol. 28(4), pages 372-375.
    11. 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.
    12. Chendi Ni & Yuying Li & Peter Forsyth & Ray Carroll, 2022. "Optimal asset allocation for outperforming a stochastic benchmark target," Quantitative Finance, Taylor & Francis Journals, vol. 22(9), pages 1595-1626, September.
    13. 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.
    14. Dimitris Politis & Halbert White, 2004. "Automatic Block-Length Selection for the Dependent Bootstrap," Econometric Reviews, Taylor & Francis Journals, vol. 23(1), pages 53-70.
    15. Shefrin, Hersh M & Thaler, Richard H, 1988. "The Behavioral Life-Cycle Hypothesis," Economic Inquiry, Western Economic Association International, vol. 26(4), pages 609-643, October.
    16. Bonnie-Jeanne MacDonald & Bruce Jones & Richard Morrison & Robert Brown & Mary Hardy, 2013. "Research and Reality: A Literature Review on Drawing Down Retirement Financial Savings," North American Actuarial Journal, Taylor & Francis Journals, vol. 17(3), pages 181-215.
    17. Peter A. Forsyth & Kenneth R. Vetzal & G. Westmacott, 2022. "Optimal performance of a tontine overlay subject to withdrawal constraints," Papers 2211.10509, arXiv.org.
    18. 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.
    19. Philippe Cogneau & Valeri Zakamouline, 2013. "Block bootstrap methods and the choice of stocks for the long run," Quantitative Finance, Taylor & Francis Journals, vol. 13(9), pages 1443-1457, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Peter A. Forsyth & Kenneth R. Vetzal & G. Westmacott, 2022. "Optimal performance of a tontine overlay subject to withdrawal constraints," Papers 2211.10509, arXiv.org.
    2. Chendi Ni & Yuying Li & Peter A. Forsyth, 2023. "Neural Network Approach to Portfolio Optimization with Leverage Constraints:a Case Study on High Inflation Investment," Papers 2304.05297, arXiv.org, revised May 2023.
    3. 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.
    4. Forsyth, Peter A., 2022. "Short term decumulation strategies for underspending retirees," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 56-74.
    5. Peter A. Forsyth, 2020. "A Stochastic Control Approach to Defined Contribution Plan Decumulation: "The Nastiest, Hardest Problem in Finance"," Papers 2008.06598, arXiv.org.
    6. Peter A. Forsyth & Kenneth R. Vetzal & Graham Westmacott, 2021. "Optimal control of the decumulation of a retirement portfolio with variable spending and dynamic asset allocation," Papers 2101.02760, arXiv.org.
    7. Li, Yuying & Forsyth, Peter A., 2019. "A data-driven neural network approach to optimal asset allocation for target based defined contribution pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 189-204.
    8. 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.
    9. Peter A. Forsyth & Kenneth R. Vetzal, 2019. "Defined Contribution Pension Plans: Who Has Seen the Risk?," JRFM, MDPI, vol. 12(2), pages 1-27, April.
    10. Chendi Ni & Yuying Li & Peter Forsyth & Ray Carroll, 2020. "Optimal Asset Allocation For Outperforming A Stochastic Benchmark Target," Papers 2006.15384, arXiv.org.
    11. Hanwen Zhang & Duy-Minh Dang, 2023. "A monotone numerical integration method for mean-variance portfolio optimization under jump-diffusion models," Papers 2309.05977, arXiv.org.
    12. van Staden, Pieter M. & Dang, Duy-Minh & Forsyth, Peter A., 2021. "The surprising robustness of dynamic Mean-Variance portfolio optimization to model misspecification errors," European Journal of Operational Research, Elsevier, vol. 289(2), pages 774-792.
    13. Peter A. Forsyth & Kenneth R. Vetzal, 2017. "Dynamic mean variance asset allocation: Tests for robustness," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-37, June.
    14. 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.
    15. Peter A. Forsyth & George Labahn, 2017. "$\epsilon$-Monotone Fourier Methods for Optimal Stochastic Control in Finance," Papers 1710.08450, arXiv.org, revised Apr 2018.
    16. P. A. Forsyth & K. R. Vetzal, 2017. "Robust Asset Allocation For Long-Term Target-Based Investing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-32, May.
    17. Liu, Lily Y. & Patton, Andrew J. & Sheppard, Kevin, 2015. "Does anything beat 5-minute RV? A comparison of realized measures across multiple asset classes," Journal of Econometrics, Elsevier, vol. 187(1), pages 293-311.
    18. E. Ramos-P'erez & P. J. Alonso-Gonz'alez & J. J. N'u~nez-Vel'azquez, 2020. "Forecasting volatility with a stacked model based on a hybridized Artificial Neural Network," Papers 2006.16383, arXiv.org, revised Aug 2020.
    19. Papantonis, Ioannis & Rompolis, Leonidas & Tzavalis, Elias, 2023. "Improving variance forecasts: The role of Realized Variance features," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1221-1237.
    20. Leippold, Markus & Vasiljević, Nikola, 2017. "Pricing and disentanglement of American puts in the hyper-exponential jump-diffusion model," Journal of Banking & Finance, Elsevier, vol. 77(C), pages 78-94.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2306.10582. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.