A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problems

In Section 3 we revisit the semi- discrete in time approximation of [10] and we improve some results, for example we prove uniform L ∞ bounds for the solutions of the

As the length of the space/time grid tends to zero, we prove several asymptotic properties of the finite MFGs equilibria and we also prove our main result showing their convergence to

On the one hand, this extension allows to cover a new type of trading strategies, such as Program Trading (executing large baskets of stocks), Arbitrage Strategies (which aims

Under suitable assumptions, if the system at time t = 0 is chaotic (that is to say the particles are independent), this chaos propa- gates as the number of particles goes to

Abstract—In this article, we develop a mean field game model for the economical analysis of the integration of purely electrical vehicles (EV) or electrical hybrid

= A)$~°~ Contrary to the QLA, the order parameter (91) correctly descnbes the entire phase diagram, from trie weak field regime (uJc < T) where the superconducting state is

Relying on classical results for the heat equation on networks and some appropriate estimates for the specific problem, we prove the well-posedness of the heat system and the

In absence of any convexity assumption, we exploit this characterization to prove convergence, as N grows, of the value functions of the centralized N -agent optimal control problem