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Deep Stochastic Optimization in Finance

Author

Listed:
  • A. Max Reppen
  • H. Mete Soner
  • Valentin Tissot-Daguette
Abstract
This paper outlines, and through stylized examples evaluates a novel and highly effective computational technique in quantitative finance. Empirical Risk Minimization (ERM) and neural networks are key to this approach. Powerful open source optimization libraries allow for efficient implementations of this algorithm making it viable in high-dimensional structures. The free-boundary problems related to American and Bermudan options showcase both the power and the potential difficulties that specific applications may face. The impact of the size of the training data is studied in a simplified Merton type problem. The classical option hedging problem exemplifies the need of market generators or large number of simulations.

Suggested Citation

  • A. Max Reppen & H. Mete Soner & Valentin Tissot-Daguette, 2022. "Deep Stochastic Optimization in Finance," Papers 2205.04604, arXiv.org.
    • Handle: RePEc:arx:papers:2205.04604
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    References listed on IDEAS

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    1. Leif Andersen & Mark Broadie, 2004. "Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options," Management Science, INFORMS, vol. 50(9), pages 1222-1234, September.
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    11. Hans Buehler & Lukas Gonon & Josef Teichmann & Ben Wood & Baranidharan Mohan & Jonathan Kochems, 2019. "Deep Hedging: Hedging Derivatives Under Generic Market Frictions Using Reinforcement Learning," Swiss Finance Institute Research Paper Series 19-80, Swiss Finance Institute.
    12. Justin Sirignano & Konstantinos Spiliopoulos, 2017. "DGM: A deep learning algorithm for solving partial differential equations," Papers 1708.07469, arXiv.org, revised Sep 2018.
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    Citations

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    Cited by:

    1. Pierre Renucci, 2023. "Optimal Linear Signal: An Unsupervised Machine Learning Framework to Optimize PnL with Linear Signals," Papers 2401.05337, arXiv.org.
    2. Josef Teichmann & Hanna Wutte, 2023. "Machine Learning-powered Pricing of the Multidimensional Passport Option," Papers 2307.14887, arXiv.org.
    3. Bernhard Hientzsch, 2023. "Reinforcement Learning and Deep Stochastic Optimal Control for Final Quadratic Hedging," Papers 2401.08600, arXiv.org.
    4. Ali Fathi & Bernhard Hientzsch, 2023. "A Comparison of Reinforcement Learning and Deep Trajectory Based Stochastic Control Agents for Stepwise Mean-Variance Hedging," Papers 2302.07996, arXiv.org, revised Nov 2023.
    5. A. Max Reppen & H. Mete Soner & Valentin Tissot-Daguette, 2022. "Neural Optimal Stopping Boundary," Papers 2205.04595, arXiv.org, revised May 2023.
    6. Anders Max Reppen & Halil Mete Soner, 2023. "Deep empirical risk minimization in finance: Looking into the future," Mathematical Finance, Wiley Blackwell, vol. 33(1), pages 116-145, January.
    7. van Staden, Pieter M. & Forsyth, Peter A. & Li, Yuying, 2024. "Across-time risk-aware strategies for outperforming a benchmark," European Journal of Operational Research, Elsevier, vol. 313(2), pages 776-800.

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