Rough Path Signatures: Learning Neural RDEs for Portfolio Optimization

Battle Count: 50

Highly relevant to quantitative trading and finance. Directly addresses portfolio optimization under path-dependent dynamics, risk-sensitive control (CVaR), and high-dimensional option pricing (Asian, barrier). The method enables solvability of path-dependent PPDEs at d>>1, which is critical for realistic multi-asset portfolio strategies. The 2BSDE/HJB framework supports dynamic allocation under stochastic volatility. However, the paper is primarily a methodological/numerical contribution rather than a trading strategy paper; practical deployment would require integration with market data pipelines and transaction cost modeling.

High complexity: requires expertise in rough path theory, log-signature computation, Neural RDE/CDE integration (adjoint methods), BSDE/2BSDE theory, Malliavin calculus, and deep learning training infrastructure. Multiple interacting components (signature encoder, RDE backbone, decoder heads, CVaR tilt, Malliavin targets, local windows, two-phase training schedule). Relies on specialized libraries (iisignature, torchcde/torchdiffeq). Hyperparameter tuning across signature depth, RDE width, window size, tilt parameters, and loss weights adds practical complexity. However, code is provided and the architecture is modular.

Code released on GitHub (https://github.com/AliAtiah/SigRDE). Fixed deterministic seeds {13,31,71,97,123} reported. Hardware (A100-40GB), software stack (PyTorch 2.x, torchdiffeq/torchcde, signature library), hyperparameters, and training schedules fully specified. Commit hashes reported. However, exact SDE parameters for all tasks and full training logs would further aid reproduction. 5-seed mean±s.e. reported for main results.