Project B04
Mean field games, rough analysis and optimal trading

Project description

This project analyzes new finite player games and mean field games (MFGs) with singular controls and common noise driven rough paths. We aim to establish new existence of equilibrium results for both finite and infinite player games and study the stability of equilibria with respect to common noise processes using rough path techniques. The project will also introduce signature-based methods for approximating extended MFGs with common noise and develop new solution techniques for forward-backward rough stochastic differential equations and quadratic mean-field BSDEs. Applications include new models of portfolio optimization with rough volatility and market impact, and extending the analysis to games with singular controls. 

Principal Investigators

Peter Friz (TU Berlin)

Ulrich Horst (HU Berlin)

Project members

Stefanos Theodorakopoulos (TU Berlin)

Huilin Zhang (HU 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)

• 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) 

• 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

• Fu, G., Hager, P. P., Horst, U., 2025. A Mean-Field Game of Market Entry: Portfolio Liquidation with Trading Constraints. https://doi.org/10.48550/arXiv.2403.10441

• 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)

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

• Denkert, R., Horst, U., 2024. Extended mean-field games with multi-dimensional singular controls and non-linear jump impact. https://doi.org/10.48550/ARXIV.2402.09317

• 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)