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The deep multi-FBSDE method: a robust deep learning method for coupled FBSDEs

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  • Kristoffer Andersson
  • Adam Andersson
  • Cornelis W. Oosterlee

Abstract

We introduce the deep multi-FBSDE method for robust approximation of coupled forward-backward stochastic differential equations (FBSDEs), focusing on cases where the deep BSDE method of Han, Jentzen, and E (2018) fails to converge. To overcome the convergence issues, we consider a family of FBSDEs that are equivalent to the original problem in the sense that they satisfy the same associated partial differential equation (PDE). Our algorithm proceeds in two phases: first, we approximate the initial condition for the FBSDE family, and second, we approximate the original FBSDE using the initial condition approximated in the first phase. Numerical experiments show that our method converges even when the standard deep BSDE method does not.

Suggested Citation

  • Kristoffer Andersson & Adam Andersson & Cornelis W. Oosterlee, 2025. "The deep multi-FBSDE method: a robust deep learning method for coupled FBSDEs," Papers 2503.13193, arXiv.org, revised May 2025.
    • Handle: RePEc:arx:papers:2503.13193
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    References listed on IDEAS

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    1. Huang, Zhipeng & Negyesi, Balint & Oosterlee, Cornelis W., 2025. "Convergence of the deep BSDE method for stochastic control problems formulated through the stochastic maximum principle," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 227(C), pages 553-568.
    2. 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.
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