Paper: arXiv 2503.13193

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.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is highly theoretical, employing advanced stochastic calculus, FBSDE theory, and rigorous numerical analysis, but lacks backtest-ready code or heavy implementation focus, showing only controlled numerical experiments.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Robust Deep Learning for Coupled FBSDEs"] --> B["Data/Input<br>FBSDE-PDE System Parameters"]
  B --> C["Methodology: Two-Phase Training"]
  C --> D["Phase 1: Approximate<br>Initial Condition via Equivalent FBSDE Family"]
  D --> E["Phase 2: Approximate<br>Original FBSDE using Initial Condition"]
  E --> F["Computational Process<br>Monte Carlo Simulation & Neural Network Optimization"]
  F --> G["Key Finding<br>Convergence Achieved where Standard Deep BSDE Method Fails"]