IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v24y2022i2d10.1007_s11009-021-09912-3.html
   My bibliography  Save this article

Deep Learning for Constrained Utility Maximisation

Author

Listed:
  • Ashley Davey

    (Imperial College)

  • Harry Zheng

    (Imperial College)

Abstract

This paper proposes two algorithms for solving stochastic control problems with deep learning, with a focus on the utility maximisation problem. The first algorithm solves Markovian problems via the Hamilton Jacobi Bellman (HJB) equation. We solve this highly nonlinear partial differential equation (PDE) with a second order backward stochastic differential equation (2BSDE) formulation. The convex structure of the problem allows us to describe a dual problem that can either verify the original primal approach or bypass some of the complexity. The second algorithm utilises the full power of the duality method to solve non-Markovian problems, which are often beyond the scope of stochastic control solvers in the existing literature. We solve an adjoint BSDE that satisfies the dual optimality conditions. We apply these algorithms to problems with power, log and non-HARA utilities in the Black-Scholes, the Heston stochastic volatility, and path dependent volatility models. Numerical experiments show highly accurate results with low computational cost, supporting our proposed algorithms.

Suggested Citation

  • Ashley Davey & Harry Zheng, 2022. "Deep Learning for Constrained Utility Maximisation," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 661-692, June.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:2:d:10.1007_s11009-021-09912-3
    DOI: 10.1007/s11009-021-09912-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-021-09912-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-021-09912-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Philipp Grohs & Fabian Hornung & Arnulf Jentzen & Philippe von Wurstemberger, 2018. "A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations," Papers 1809.02362, arXiv.org, revised Jan 2023.
    2. Shuaiqiang Liu & Cornelis W. Oosterlee & Sander M. Bohte, 2019. "Pricing Options and Computing Implied Volatilities using Neural Networks," Risks, MDPI, vol. 7(1), pages 1-22, February.
    3. Lukas Gonon & Johannes Muhle-Karbe & Xiaofei Shi, 2019. "Asset Pricing with General Transaction Costs: Theory and Numerics," Papers 1905.05027, arXiv.org, revised Apr 2020.
    4. Jan De Spiegeleer & Dilip B. Madan & Sofie Reyners & Wim Schoutens, 2018. "Machine learning for quantitative finance: fast derivative pricing, hedging and fitting," Quantitative Finance, Taylor & Francis Journals, vol. 18(10), pages 1635-1643, October.
    5. Ma, Jingtang & Li, Wenyuan & Zheng, Harry, 2020. "Dual control Monte-Carlo method for tight bounds of value function under Heston stochastic volatility model," European Journal of Operational Research, Elsevier, vol. 280(2), pages 428-440.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ashley Davey & Harry Zheng, 2024. "Deep Learning Methods for S Shaped Utility Maximisation with a Random Reference Point," Papers 2410.05524, arXiv.org.

    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. Ashley Davey & Harry Zheng, 2020. "Deep Learning for Constrained Utility Maximisation," Papers 2008.11757, arXiv.org, revised Aug 2021.
    2. Kathrin Glau & Linus Wunderlich, 2020. "The Deep Parametric PDE Method: Application to Option Pricing," Papers 2012.06211, arXiv.org.
    3. Shuaiqiang Liu & Anastasia Borovykh & Lech A. Grzelak & Cornelis W. Oosterlee, 2019. "A neural network-based framework for financial model calibration," Papers 1904.10523, arXiv.org.
    4. Glau, Kathrin & Wunderlich, Linus, 2022. "The deep parametric PDE method and applications to option pricing," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    5. Timothy DeLise, 2021. "Neural Options Pricing," Papers 2105.13320, arXiv.org.
    6. Sina Montazeri & Akram Mirzaeinia & Haseebullah Jumakhan & Amir Mirzaeinia, 2024. "CNN-DRL for Scalable Actions in Finance," Papers 2401.06179, arXiv.org.
    7. Patrick Büchel & Michael Kratochwil & Maximilian Nagl & Daniel Rösch, 2022. "Deep calibration of financial models: turning theory into practice," Review of Derivatives Research, Springer, vol. 25(2), pages 109-136, July.
    8. Kim, Jong-Min & Kim, Dong H. & Jung, Hojin, 2021. "Applications of machine learning for corporate bond yield spread forecasting," The North American Journal of Economics and Finance, Elsevier, vol. 58(C).
    9. Junike, Gero & Pankrashkin, Konstantin, 2022. "Precise option pricing by the COS method—How to choose the truncation range," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    10. Sangseop Lim & Chang-hee Lee & Won-Ju Lee & Junghwan Choi & Dongho Jung & Younghun Jeon, 2022. "Valuation of the Extension Option in Time Charter Contracts in the LNG Market," Energies, MDPI, vol. 15(18), pages 1-14, September.
    11. Polyzos, Stathis & Samitas, Aristeidis & Katsaiti, Marina-Selini, 2020. "Who is unhappy for Brexit? A machine-learning, agent-based study on financial instability," International Review of Financial Analysis, Elsevier, vol. 72(C).
    12. Sebastian Jaimungal, 2022. "Reinforcement learning and stochastic optimisation," Finance and Stochastics, Springer, vol. 26(1), pages 103-129, January.
    13. Kamma, Thijs & Pelsser, Antoon, 2022. "Near-optimal asset allocation in financial markets with trading constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 766-781.
    14. Isaenko, Sergey, 2023. "Transaction costs, frequent trading, and stock prices," Journal of Financial Markets, Elsevier, vol. 64(C).
    15. Lokeshwar, Vikranth & Bharadwaj, Vikram & Jain, Shashi, 2022. "Explainable neural network for pricing and universal static hedging of contingent claims," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    16. Maximilien Germain & Huyên Pham & Xavier Warin, 2021. "Neural networks-based algorithms for stochastic control and PDEs in finance ," Post-Print hal-03115503, HAL.
    17. Bauer, Kevin & Nofer, Michael & Abdel-Karim, Benjamin M. & Hinz, Oliver, 2022. "The effects of discontinuing machine learning decision support," SAFE Working Paper Series 370, Leibniz Institute for Financial Research SAFE.
    18. Johannes Muhle-Karbe & Xiaofei Shi & Chen Yang, 2020. "An Equilibrium Model for the Cross-Section of Liquidity Premia," Papers 2011.13625, arXiv.org.
    19. Goudenège, Ludovic & Molent, Andrea & Zanette, Antonino, 2022. "Moving average options: Machine learning and Gauss-Hermite quadrature for a double non-Markovian problem," European Journal of Operational Research, Elsevier, vol. 303(2), pages 958-974.
    20. Sandrine Gumbel & Thorsten Schmidt, 2020. "Machine learning for multiple yield curve markets: fast calibration in the Gaussian affine framework," Papers 2004.07736, arXiv.org, revised Apr 2020.

    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:spr:metcap:v:24:y:2022:i:2:d:10.1007_s11009-021-09912-3. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.