Paper: arXiv 2510.10728

Authors: Ali Atiah Alzahrani

Abstract

We tackle high-dimensional, path-dependent valuation and control and introduce a deep BSDE/2BSDE solver that couples truncated log-signatures with a neural rough differential equation (RDE) backbone. The architecture aligns stochastic analysis with sequence-to-path learning: a CVaR-tilted terminal objective targets left-tail risk, while an optional second-order (2BSDE) head supplies curvature estimates for risk-sensitive control. Under matched compute and parameter budgets, the method improves accuracy, tail fidelity, and training stability across Asian and barrier option pricing and portfolio control: at d=200 it achieves CVaR(0.99)=9.80% versus 12.00-13.10% for strong baselines, attains the lowest HJB residual (0.011), and yields the lowest RMSEs for Z and Gamma. Ablations over truncation depth, local windows, and tilt parameters confirm complementary gains from the sequence-to-path representation and the 2BSDE head. Taken together, the results highlight a bidirectional dialogue between stochastic analysis and modern deep learning: stochastic tools inform representations and objectives, while sequence-to-path models expand the class of solvable financial models at scale.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a sophisticated theoretical framework coupling rough path log-signatures with Neural RDEs and 2BSDEs to solve high-dimensional path-dependent financial problems. It demonstrates strong empirical rigor with benchmarks up to d=200, extensive metric evaluations (CVaR, HJB residuals, RMSEs), and provides a public code repository for reproducibility.

Research Flowchart

  flowchart TD
    A[Goal: Solve High-Dimensional, Path-Dependent Financial Control & Valuation] --> B[Inputs: Asset Paths, Tail Loss Objective CVaR, BSDE/2BSDE Inputs]
    B --> C[Method: Truncate Log-Signatures & Neural RDE Backbone]
    C --> D[Compute: Train Neural RDE with CVaR-Tilted Loss & 2BSDE Curvature Head]
    D --> E[Outcome: Scaled to d=200, Reduced Tail Risk CVaR=9.80%, Lowest HJB Residual 0.011]

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0 of 30 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.