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math.AP2023
Stochastic optimal transport and Hamilton-Jacobi-Bellman equations on the set of probability measures
Charles Bertucci
We introduce a stochastic version of the optimal transport problem. We provide an analysis by means of the study of the associated Hamilton-Jacobi-Bellman equation, which is set on…
math.AP2023
On Lipschitz solutions of mean field games master equations
Charles Bertucci, Jean-Michel Lasry, Pierre-Louis Lions
We develop a theory of existence and uniqueness of solutions of MFG master equations when the initial condition is Lipschitz continuous. Namely, we show that as long as the solutio…