Project A07
Rough backward stochastic differential equations

Project description

Recent developments show an increasing integration of concepts from rough and stochastic analysis. We focus on classes of backward stochastic differential equations (BSDEs) with less regularity than classical theory. This project explores BSDEs with hybrid dynamics, incorporating both stochastic and rough driving noises. We particularly emphasize the stability of such equations, including BSDEs with rough jump noise and hybrid rough stochastic forward processes. Moreover, the project examines the connection to semilinear singular PDEs. 

Principal Investigators

Dirk Becherer (HU Berlin)

Peter Friz (TU Berlin)

Project members

Yuchen Sun (HU & TU Berlin)

Publications

• Friz, P.K., Kern, H., Zorin-Kranich, P., 2025. Lipschitz estimates in the Besov settings for Young and rough differential equations. Journal of Differential Equations 443, 113507. https://doi.org/10.1016/j.jde.2025.113507 (A02, A07, B04)

• 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

• Becherer, D., Sun, Y., 2025. Rough backward SDEs with discontinuous Young drivers. https://doi.org/10.48550/ARXIV.2505.20437

• Friz, P.K., Lê, K., Zhang, H., 2024. Controlled rough SDEs, pathwise stochastic control and dynamic programming principles. https://doi.org/10.48550/ARXIV.2412.05698 (A07, B04, B05)