From the 1 of 6 linked papers with an AI index.
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Analysis on spaces of measures
Charles Bertucci
This work presents analytical tools for studying functions defined on spaces of measures, together with two applications: mean field game master equations and first order Hamilton-…
Non-linear Stegall's lemma and general Hamilton-Jacobi-Bellman equations on Wasserstein spaces
Charles Bertucci, Pierre-Louis Lions
We present a comparison principle for unbounded viscosity solutions to Hamilton-Jacobi equations on Wasserstein spaces of probability measures over . In addition to the use o…
Mean field games with incomplete information
Charles Bertucci
This paper is concerned with mean field games in which the players do not know the repartition of the other players. First a case in which the players do not gain information is st…
The equilibrium price of bubble assets
Charles Bertucci, Jean-Michel Lasry, Pierre Louis Lions
Considering a simple economy, we derive a new Hamilton-Jacobi equation which is satisfied by the value of a ''bubble'' asset. We then show, by providing a rigorous mathematical ana…
A study of common noise in mean field games
Charles Meynard, Charles Bertucci
This paper is concerned with the study of mean field games master equations involving an additional variable modelling common noise. We address cases in which the dynamics of this…
An approximation of the squared Wasserstein distance and an application to Hamilton-Jacobi equations
Charles Bertucci, Pierre Louis Lions
We provide a simple approximation of the squared Wasserstein distance on R^d when one of the two measures is fixed. This approximation converges locally uniformly. More i…