Mathematical Finance Seminar
Date
Time
16:15
Location
HUB; RUD 25; 1.115
Frederico Cannerozzi (Bielefeld)
Singular Mean-Field Control via singular Mean-Field Games
Mean-field control (MFC) and mean-field games (MFGs) provide two different descriptions of large interacting populations: in MFC, a central planner optimizes the collective performance of the system, while in MFGs each representative player optimizes individually against a given population distribution, which is then determined through a consistency condition. In general, the corresponding optimal controls and equilibria need not coincide. A much tighter connection is known for potential mean-field games: an MFG equilibrium can be obtained by solving an associated auxiliary mean-field control problem. This naturally suggests the reverse question: can a mean-field control problem be solved by means of an auxiliary potential mean-field game? We discuss this approach in two settings of mean-field control with singular controls, where the associated potential MFG can provide a tractable route to the original MFC problem. In a stationary Ornstein-Uhlenbeck model with two-sided singular controls, we obtain a two-way correspondence between the MFC problem and an associated potential MFG. In a finite-horizon framework with general dependence on the state distribution, we show that equilibria of the associated potential MFG yield optimal controls for the MFC problem, and illustrate the approach through a mean-field monotone follower problem.