Project B05
Rough analysis in stochastic control

Project description

This project develops tools to analyze how control problems in finance, including those with mean-field components, depend on noise paths. Focusing on rough noises, it goes beyond traditional semi-martingale models. The project combines dynamic programming, maximum principles, and duality methods to establish stability of optimal strategies and value functions with respect to rough paths, improving our understanding of path-wise versus stochastic control. 

Principal Investigators

Peter Bank (TU Berlin)

Ulrich Horst (HU Berlin)

Project members

Filippo de Feo (TU Berlin)

Huilin Zhang (HU Berlin)

Publications

• Denkert, R., Horst, U., 2025. Extended Mean-Field Games with Multidimensional Singular Controls and Nonlinear Jump Impact. SIAM J. Control Optim. 63, 1374–1406. https://doi.org/10.1137/24M1640860 (B04, B05) 

• De Feo, F., Święch, A., 2025. Optimal control of stochastic delay differential equations: Optimal feedback controls. Journal of Differential Equations 420, 450–508. https://doi.org/10.1016/j.jde.2024.12.019

• De Feo, F., Święch, A., Wessels, L., 2025. Stochastic optimal control in Hilbert spaces: C1,1 regularity of the value function and optimal synthesis via viscosity solutions. Electron. J. Probab. 30. https://doi.org/10.1214/25-EJP1294

Preprints

• Denkert, R., Horst, U., 2025. Mean-field control problems with multi-dimensional singular controls. https://doi.org/10.48550/arXiv.2308.04378

• Horst, U., Zhang, H., 2025. Pontryagin Maximum Principle for rough stochastic systems and pathwise stochastic control. https://doi.org/10.48550/ARXIV.2503.22959 (B04, B05)

• de Feo, F., Federico, S., Gozzi, F., Touzi, N., 2024. Sensitivity of functionals of McKean-Vlasov SDE’s with respect to the initial distribution. https://doi.org/10.48550/ARXIV.2412.15906  (latest version April 2025)

• Friz, P.K., Le, K., Zhang, H., 2025. Randomisation of rough stochastic differential equations. https://doi.org/10.48550/ARXIV.2503.06622 (B04, B05)

• de Crescenzo, A., de Feo, F., Pham, H., 2025. Linear-quadratic optimal control for non-exchangeable mean-field SDEs and applications to systemic risk. https://doi.org/10.48550/ARXIV.2503.03318 

• de Feo, F., 2025. Stochastic optimal control problems with measurable coefficients via $L^p$-viscosity solutions and applications to optimal advertising models. https://doi.org/10.48550/ARXIV.2502.02352 

• 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)