Convergence of a Deep BSDE solver with jumps

ArXiv ID: 2501.09727 “View on arXiv”

Authors: Unknown

Abstract

We study the error arising in the numerical approximation of FBSDEs and related PIDEs by means of a deep learning-based method. Our results focus on decoupled FBSDEs with jumps and extend the seminal work of HAn and Long (2020) analyzing the numerical error of the deep BSDE solver proposed in E et al. (2017). We provide a priori and a posteriori error estimates for the finite and infinite activity case.

Keywords: FBSDEs, Deep Learning, PIDEs, Error Estimates, Numerical Approximation, Derivatives Pricing

Complexity vs Empirical Score

• Math Complexity: 9.2/10
• Empirical Rigor: 3.5/10
• Quadrant: Lab Rats
• Why: The paper presents highly advanced stochastic analysis, PIDE theory, and deep learning convergence proofs, reflecting deep mathematical complexity. It lacks any reported backtests, numerical experiments, or implementation details, focusing solely on theoretical error estimates.

  flowchart TD
    A["<b>Research Goal:</b><br>Estimation of numerical errors in<br>Deep BSDE solver for FBSDEs with jumps"] --> B["<b>Methodology:</b><br>Extended analysis of HAn & Long (2020)<br>Applied to decoupled FBSDEs"]
    B --> C["<b>Inputs/Targets:</b><br>Finite & Infinite Activity Jump Processes<br>Related Parabolic Integro-Differential Eqs (PIDEs)"]
    C --> D["<b>Computational Process:</b><br>Deep Learning-based BSDE Solver<br>(E et al. 2017 framework)"]
    D --> E
    subgraph E ["Outcomes"]
        F["<b>A Priori Error Estimates</b>"]
        G["<b>A Posteriori Error Estimates</b>"]
    end