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.
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
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)