12 citations · 20 across the 13 of their papers we have counts for
12 papers · 1 filter
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…
A Spectral Dominance Approach to Large Random Matrices
Charles Bertucci, Mérouane Debbah, Jean-Michel Lasry +1
This paper presents a novel approach to characterize the dynamics of the limit spectrum of large random matrices. This approach is based upon the notion we call "spectral dominance…
Dimension reduction techniques in deterministic mean field games
Jean-Michel Lasry, Pierre-Louis Lions, Benjamin Seeger
We present examples of equations arising in the theory of mean field games that can be reduced to a system in smaller dimensions. Such examples come up in certain applications, and…
A class of short-term models for the oil industry addressing speculative storage
Yves Achdou, Charles Bertucci, Jean-Michel Lasry +3
This is a work in progress. The aim is to propose a plausible mechanism for the short term dynamics of the oil market based on the interaction of economic agents. This is a theoret…
Master equation for the finite state space planning problem
Charles Bertucci, Jean-Michel Lasry, Pierre-Louis Lions
We present results of existence, regularity and uniqueness of solutions of the master equation associated with the mean field planning problem in the finite state space case, in th…
Strategic advantages in mean field games with a major player
Charles Bertucci, Jean-Michel Lasry, Pierre-Louis Lions
This note is concerned with a modeling question arising from the mean field games theory. We show how to model mean field games involving a major player which has a strategic advan…
Some remarks on Mean Field Games
Charles Bertucci, Jean Michel Lasry, Pierre Louis Lions
We study in this paper three aspects of Mean Field Games. The first one is the case when the dynamics of each player depend on the strategies of the other players. The second one c…
The master equation and the convergence problem in mean field games
Pierre Cardaliaguet, François Delarue, Jean-Michel Lasry +1
The paper studies the convergence, as tends to infinity, of a system of coupled Hamilton-Jacobi equations, the Nash system. This system arises in differential game theory.…