# Rough Path Signatures: Learning Neural RDEs for Portfolio Optimization

arXiv: https://arxiv.org/abs/2510.10728 · HTML: https://mlsanity.com/paper/2510.10728/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 28 references that are in the map.
- First posted on arXiv 12 Oct 2025.

## Builds on (most cited first, 10 of 10)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Neural Rough Differential Equations for Long Time Series](https://mlsanity.com/paper/2009.08295/) (2020)
- [A Primer on the Signature Method in Machine Learning](https://mlsanity.com/paper/1603.03788/) (2016)
- [Deep Signature Transforms](https://mlsanity.com/paper/1905.08494/) (2019)
- [Deep splitting method for parabolic PDEs](https://mlsanity.com/paper/1907.03452/) (2019)
- [The iisignature library: efficient calculation of iterated-integral signatures and log signatures](https://mlsanity.com/paper/1802.08252/) (2018)
- [Neural networks-based backward scheme for fully nonlinear PDEs](https://mlsanity.com/paper/1908.00412/) (2019)
- [A Neural RDE-based model for solving path-dependent PDEs](https://mlsanity.com/paper/2306.01123/) (2023)

## Abstract (arXiv)

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.