Paper: arXiv 2601.18634

Authors: Zhipeng Huang, Cornelis W. Oosterlee

Abstract

We propose the Compound BSDE method, a fully forward, deep-learning-based approach for solving a broad class of problems in financial mathematics, including optimal stopping. The method is based on a reformulation of option pricing problems in terms of a system of backward stochastic differential equations (BSDEs), which offers a new perspective on the numerical treatment of compound options and optimal stopping problems such as Bermudan option pricing. Building on the classical deep BSDE method for a single BSDE, we develop an algorithm for compound BSDEs and establish its convergence properties. In particular, we derive an a posteriori error estimate for the proposed method. Numerical experiments demonstrate the accuracy and computational efficiency of the approach, and illustrate its effectiveness for high-dimensional option pricing and optimal stopping problems.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 4.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides strong theoretical foundations, including a rigorous proof of convergence and error estimates for solving coupled systems of BSDEs via deep learning. However, it leans primarily theoretical, with empirical evaluation limited to simulated numerical examples rather than real-world market datasets.

Research Flowchart

  flowchart TD
    A[Goal: Solve High-Dimensional Optimal Stopping & Option Pricing] --> B[Inputs: Financial Assets & Bermudan/Compound Option Terms]
    B --> C[Reformulate Problem into a Compound System of BSDEs]
    C --> D[Apply Fully Forward Deep Learning Algorithm]
    D --> E[Derive A Posteriori Error Estimates]
    E --> F[Numerical Experiments & High-Dimensional Validation]
    F --> G[Outcomes: Accurate, Efficient Pricing with Convergence Guarantees]

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2 of 92 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.