Stochastic Optimal Control

The group studies various problems of stochastic optimal control by means of different methodologies. More precisely, stochastic optimal control problems on finite or infinite horizon are studied, as well as optimal stopping problems and related free boundary problems, problems with switching, singular or impulsive control, robust optimal control problems, ergodic optimal control problems. Those control problems are investigated in the presence of some non-standard features, which turn out to be relevant for the applications: this is the case for instance of control problems with path-dependence or delay in the state variable, with partial observation, with mean field interaction or McKean-Vlasov dynamics. The main methodologies implemented are dynamic programming and backward stochastic differential equations' methods. Particular attention is devoted to the study of the corresponding Hamilton-Jacobi-Bellman equations in the Wasserstein space of in the space of continuous paths, where suitable notions of viscosity solution are adopted.

Faculty:

Elena Bandini

Senior assistant professor (fixed-term)

Stefano Pagliarani

Associate Professor

Andrea Pascucci

Full Professor

Antonello Pesce

Junior assistant professor (fixed-term)

Research Fellows and Ph.D. Students:

Elisa Raspanti

PhD Student

External Collaborators:

Erhan Bayraktar, Marco Fuhrman, Fausto Gozzi, Idris Kharroubi, Huyên Pham, Francesco Russo, Gianmario Tessitore.