12 citations · 20 across the 13 of their papers we have counts for
17 papers
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…
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 spectral dominance approach to large random matrices: part II
Charles Bertucci, Jean-Michel Lasry, Pierre Louis Lions
This paper is the second of a series devoted to the study of the dynamics of the spectrum of large random matrices. We study general extensions of the partial differential equation…
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…
Simulating numerically the Krusell-Smith model with neural networks
Yves Achdou, Jean-Michel Lasry, Pierre Louis Lions
The celebrated Krusel-Smith growth model is an important example of a Mean Field Game with a common noise. The Mean Field Game is encoded in the master equation, a partial differen…
A singular infinite dimensional Hamilton-Jacobi-Bellman equation arising from a storage problem
Charles Bertucci, Jean-Michel Lasry, Pierre Louis Lions
In the first part of this paper, we derive an infinite dimensional partial differential equation which describes an economic equilibrium in a model of storage which includes an inf…