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

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

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