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Asymptotic Expansion as Prior Knowledge in Deep Learning Method for High dimensional BSDEs

Author

Listed:
  • Masaaki Fujii

    (The University of Tokyo)

  • Akihiko Takahashi

    (The University of Tokyo)

  • Masayuki Takahashi

    (The University of Tokyo)

Abstract

We demonstrate that the use of asymptotic expansion as prior knowledge in the “deep BSDE solver”, which is a deep learning method for high dimensional BSDEs proposed by Weinan et al. (Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations, 2017b. arXiv:1706.04702 ), drastically reduces the loss function and accelerates the speed of convergence. We illustrate the technique and its implications by using Bergman’s model with different lending and borrowing rates as a typical model for FVA as well as a class of solvable BSDEs with quadratic growth drivers. We also present an extension of the deep BSDE solver for reflected BSDEs representing American option prices.

Suggested Citation

  • Masaaki Fujii & Akihiko Takahashi & Masayuki Takahashi, 2019. "Asymptotic Expansion as Prior Knowledge in Deep Learning Method for High dimensional BSDEs," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 26(3), pages 391-408, September.
    • Handle: RePEc:kap:apfinm:v:26:y:2019:i:3:d:10.1007_s10690-019-09271-7
    DOI: 10.1007/s10690-019-09271-7
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    References listed on IDEAS

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