12 citations · 27 across the 23 of their papers we have counts for
28 papers
Optimal control of the Dyson equation
Charles Bertucci, Pierre-Louis Lions, Panagiotis E. Souganidis
We provide a complete study of the optimal control problem associated to the so-called Dyson equation, which describes the mean field evolution of the spectrum of large random matr…
Wasserstein spaces have the Radon-Nikodym property
Charles Bertucci
Wasserstein spaces carry two natural geometries: a vertical one, inherited from the linear structure of signed measures, and a horizontal one, induced by couplings. We prove that a…
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-…
Infinite horizon stochastic optimal control with sign-changing discount factor
Charles Bertucci, Jean-Michel Lasry, Pierre-Louis Lions
We study an infinite horizon stochastic optimal control problem by means of the associated Hamilton-Jacobi-Bellman equation. The problem we are studying has the particularity of ha…
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…
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…