Rough Path Signatures: Learning Neural RDEs for Portfolio Optimization

• URL: http://arxiv.org/abs/2510.10728v3
• Date: Mon, 03 Nov 2025 12:33:09 GMT
• Title: Rough Path Signatures: Learning Neural RDEs for Portfolio Optimization
• Abstract summary: We introduce a deep BSDE/2BSDE solver that couples truncated log-signatures with a neural rough differential equation backbone.<n>The architecture aligns objective analysis with sequence-to-path learning: a CVaR-tilted terminal targets left-tail risk, while an optional second-order (2BSDE) head supplies curvature estimates for risk-sensitive control.<n>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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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