Speaker: Luciano Campi
Title: Mean Field Games with Terminal State Constraints
Abstract: We study a mean field game (MFG) with state dynamics described by stochastic differential equations affected by both idiosyncratic and common noise, and subject to the constraint that the terminal state variable should belong to a given nonempty convex closed set. Moreover, the mean field interaction enters through both state and controls in the dynamics and the costs. Inspired by the works of El Karoui, Peng, Quenez [Ann. Appl. Prob., 11(3), 2001], and Ji and Zhou [Comm. Inf. Syst. 6(4), 2006], we establish an auxiliary MFG problem and derive the stochastic maximum principle for the associated optimization problem under fixed flows. Additionally, we apply our approach to (a perturbation of) a MFG of optimal liquidation and a MFG of optimal investment with a quadratic relative performance criterion. This talk is based on a joint work in progress with L. Di Persio (Verona University) and V. Vardanyan (Trento University).