Project B03
Signature methods for optimal control in finance

Project description

This project aims to construct and analyze numerical methods for stochastic optimal control problems in finance using the path signature. Traditional methods, often relying on Markov processes, face challenges with path-dependent cases due to the curse of dimensionality. The signature provides a means to extend these techniques to non-Markovian problems by efficiently encoding the path's history. Our focus will be on simulation-based methods, developing general approximation methods for optimal controls and efficient numerical methods for BSDEs, even in non-Markovian systems, along with in-depth quantitative error estimates. 

Principal Investigators

Peter Bank (TU Berlin)

Christian Bayer (WIAS)

Project members

Marco Rodrigues (WIAS & TU Berlin)

Alumni

Luca Pelizzari (WIAS & TU Berlin)

Publications

• Bank, P., Bayer, C., Friz, P.K., Pelizzari, L., 2025. Rough PDEs for Local Stochastic Volatility Models. Mathematical Finance mafi.12458. https://doi.org/10.1111/mafi.12458 (A07, B02, B03, B04)

Preprints

• Aqsha, A., Bank, P., & Sánchez-Betancourt, L., 2026. Solving linear-quadratic stochastic control problems with signatures. https://doi.org/10.48550/arXiv.2602.23473 

• Bank, P., & de Feo, F., 2026. Duality methods in stochastic optimal control. https://doi.org/10.48550/ARXIV.2602.17823 (B03, B05)

• Bayer, C., Ben Naamia, S., von Schwerin, E., & Tempone, R. 2025. A Pontryagin Maximum Principle on the Belief Space for Continuous-Time Optimal Control with Discrete Observations. https://doi.org/10.48550/ARXIV.2512.24916

• Bayer, C., Gogolashvili, D., & Pelizzari, L. 2025. Local Regression on Path Spaces with Signature Metrics. https://doi.org/10.48550/ARXIV.2510.16728 (B01, B03)

• Bayer, C., Pelizzari, L., & Zhu, J.-J., 2025. Pricing American options under rough volatility using deep-signatures and signature-kernels. https://doi.org/10.48550/ARXIV.2501.06758 (B01, B03)

• Bayer, C., & Redmann, M., 2024. Dimension reduction for path signatures. https://doi.org/10.48550/ARXIV.2412.14723 (B01, B03)

• Bayer, C., Djehiche, B., Rezvanova, E., & Tempone, R. F., 2024. Continuous time Stochastic optimal control under discrete time partial observations. https://doi.org/10.48550/ARXIV.2407.18018