Convergence of the Deep BSDE method for FBSDEs with non-Lipschitz coefficients
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Abstract (arXiv)
This paper is dedicated to solving high-dimensional coupled FBSDEs with non-Lipschitz diffusion coefficients numerically. Under mild conditions, we provided a posterior estimate of the numerical solution that holds for any time duration. This posterior estimate validates the convergence of the recently proposed Deep BSDE method. In addition, we developed a numerical scheme based on the Deep BSDE method and presented numerical examples in financial markets to demonstrate the high performance.
Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). First posted on arXiv 6 Jan 2021.
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Citing papers per year: 2021: 1; 2022: 1; 2023: 3; 2024: 1; 2025: 1.
7 papers.
- 2021Solving high-dimensional parabolic PDEs using the tensor train formatcited by 17
- 2022Convergence of a robust deep FBSDE method for stochastic controlcited by 11
- 2023From continuous-time formulations to discretization schemes: tensor trains and robust regression for BSDEs and parabolic PDEscited by 5
- 2024A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equationscited by 4
- 2023Uncertainty quantification for deep learning-based schemes for solving high-dimensional backward stochastic differential equationscited by 1
- 2023Deep Generative Modeling with Backward Stochastic Differential Equationscited by 0
- 2025Error analysis for the deep Kolmogorov methodcited by 0
- 2025Error analysis for the deep Kolmogorov method23 Aug 2025
- 2024A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations12 Apr 2024
- 2023Uncertainty quantification for deep learning-based schemes for solving high-dimensional backward stochastic differential equations5 Oct 2023
- 2023From continuous-time formulations to discretization schemes: tensor trains and robust regression for BSDEs and parabolic PDEs28 Jul 2023
- 2023Deep Generative Modeling with Backward Stochastic Differential Equations8 Apr 2023
- 2022Convergence of a robust deep FBSDE method for stochastic control18 Jan 2022
- 2021Solving high-dimensional parabolic PDEs using the tensor train format23 Feb 2021