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An acceleration scheme for deep learning-based BSDE solver using weak expansions

Author

Listed:
  • Riu Naito

    (Asset Management One Co., Ltd., Chiyoda-ku, Tokyo, Japan)

  • Toshihiro Yamada

    (#x2020;Graduate School of Economics, Hitotsubashi University, Tokyo, Japan)

Abstract

This paper gives an acceleration scheme for deep backward stochastic differential equation (BSDE) solver, a deep learning method for solving BSDEs introduced in Weinan et al. [Weinan, E, J Han and A Jentzen (2017). Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations, Communications in Mathematics and Statistics, 5(4), 349–380]. The solutions of nonlinear partial differential equations are quickly estimated using technique of weak approximation even if the dimension is high. In particular, the loss function and the relative error for the target solution become sufficiently small through a smaller number of iteration steps in the new deep BSDE solver.

Suggested Citation

  • Riu Naito & Toshihiro Yamada, 2020. "An acceleration scheme for deep learning-based BSDE solver using weak expansions," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(02), pages 1-12, June.
    • Handle: RePEc:wsi:ijfexx:v:07:y:2020:i:02:n:s2424786320500127
    DOI: 10.1142/S2424786320500127
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    Citations

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    Cited by:

    1. Akihiko Takahashi & Yoshifumi Tsuchida & Toshihiro Yamada, 2021. "A new efficient approximation scheme for solving high-dimensional semilinear PDEs: control variate method for Deep BSDE solver," CARF F-Series CARF-F-504, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jan 2022.
    2. Akihiko Takahashi & Yoshifumi Tsuchida & Toshihiro Yamada, 2022. "A new efficient approximation scheme for solving high-dimensional semilinear PDEs: control variate method for Deep BSDE solver (Journal of Computational Physics, published online 19 January 2022)," CARF F-Series CARF-F-532, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Feb 2022.
    3. Akihiko Takahashi & Yoshifumi Tsuchida & Toshihiro Yamada, 2021. "A new efficient approximation scheme for solving high-dimensional semilinear PDEs: control variate method for Deep BSDE solver," Papers 2101.09890, arXiv.org, revised Jan 2021.
    4. Rawin Assabumrungrat & Kentaro Minami & Masanori Hirano, 2023. "Error Analysis of Option Pricing via Deep PDE Solvers: Empirical Study," Papers 2311.07231, arXiv.org.
    5. Akihiko Takahashi & Yoshifumi Tsuchida & Toshihiro Yamada, 2021. "A New Efficient Approximation Scheme for Solving High-Dimensional Semilinear PDEs: Control Variate Method for Deep BSDE Solver," CIRJE F-Series CIRJE-F-1159, CIRJE, Faculty of Economics, University of Tokyo.
    6. Yoshifumi Tsuchida, 2023. "Control Variate Method for Deep BSDE Solver Using Weak Approximation," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 30(2), pages 273-296, June.

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