On the Optimal Control of McKean Vlasov SDE and Mean Field Games in Infinite Dimension

PDE Seminar
Tuesday, January 10, 2023 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 006
Fausto Gozzi – Luiss University – fgozzi@luiss.ithttp://docenti.luiss.it/gozzi/chi-sono/
Gong Chen

In this talk we report on recent works (with A. Cosso, I. Kharroubi, H. Pham, M. Rosestolato) on the optimal control of (possibly path dependent) McKean-Vlasov equations valued in Hilbert spaces. On the other side we present the first ideas of a work with S. Federico, D. Ghilli and M. Rosestolato, on Mean Field Games in infinite dimension.

We will begin by presenting some examples for both topics and their relations. Then most of the time will be devoted to the first topic and the main results (the dynamic programming principle, the law invariance property of the value function, the Ito formula and the fact that the value function is a viscosity solution of the HJB equation, a first comparison result).

We conclude, if time allows, with the first ideas on the solution of the HJB-FKP system arising in mean Field Games in infinite dimension.