Paper: arXiv 2511.08735

Authors: Hasib Uddin Molla, Matthew Backhouse, Ankit Banarjee, Jinniao Qiu

Abstract

In this work, we extend deep learning-based numerical methods to fully coupled forward-backward stochastic differential equations (FBSDEs) within a non-Markovian framework. Error estimates and convergence are provided. In contrast to the existing literature, our approach not only analyzes the non-Markovian framework but also addresses fully coupled settings, in which both the drift and diffusion coefficients of the forward process may be random and depend on the backward components $Y$ and $Z$. Furthermore, we illustrate the practical applicability of our framework by addressing utility maximization problems under rough volatility, which are solved numerically with the proposed deep learning-based methods.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical extension of Deep BSDE algorithms to fully coupled, non-Markovian FBSDEs with formal convergence proofs and error estimates. However, its empirical validation is purely synthetic and numerical, lacking real-world financial dataset backtests or empirical market evaluations.

Research Flowchart

  flowchart TD
    A[Research Goal: Solve Fully Coupled Non-Markovian FBSDEs via Deep Learning] --> B[Input: Random Drift/Diffusion dependent on Y & Z, Rough Volatility]
    B --> C[Methodology: Extend Deep Learning Methods to Fully Coupled Non-Markovian Setting]
    C --> D[Computational Process: Neural Network Approximation & Error Estimation]
    D --> E[Application: Numerical Simulation of Utility Maximization under Rough Volatility]
    E --> F[Outcomes: Rigorous Convergence Proofs & Efficient High-Dimensional Solver]

Cited References (29)

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  8. Finding adapted solutions of forward-backward stochastic differential equations: method of continuation (1997)
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0 of 29 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.