The theory of mean field games (MFGs) studies the limiting behaviors of large systems
where the agents interact with each other in a certain symmetric way. The running and …

In this manuscript we construct global in time classical solutions to mean field games master
equations in the lack of idiosyncratic noise in the individual agents' dynamics. These include …

We consider linear and nonlinear transport equations with irregular velocity fields, motivated
by models coming from mean field games. The velocity fields are assumed to increase in …

In this manuscript, we study a class of linear-quadratic (LQ) mean field control problems with
a common noise and their corresponding $ N $-particle systems. The mean field control …

We prove well-posedness of a class of kinetic-type Mean Field Games, which typically arise
when agents control their acceleration. Such systems include independent variables …

This paper studies relative arbitrage opportunities in a market with infinitely many interacting
investors. We establish a conditional McKean-Vlasov system to study the market dynamics …

Here Xi=(Xi (t)) t≥ 0 is the i-th player's state process driven by the noise process Wi=(Wi (t))
t∈≥ 0 and subject to all players' strategies (v1,···, vN). Each player has the individual …