[图书][B] Probabilistic theory of mean field games with applications I-II
The lion's share of this chapter is devoted to the construction of equilibria for mean field
games with a common noise. We develop a general two-step strategy for the search of weak …
games with a common noise. We develop a general two-step strategy for the search of weak …
An introduction to mean field game theory
These notes are an introduction to Mean Field Game (MFG) theory, which models differential
games involving infinitely many interacting players. We focus here on the Partial Differential …
games involving infinitely many interacting players. We focus here on the Partial Differential …
Stochastic graphon games: Ii. the linear-quadratic case
In this paper, we analyze linear-quadratic stochastic differential games with a continuum of
players interacting through graphon aggregates, each state being subject to idiosyncratic …
players interacting through graphon aggregates, each state being subject to idiosyncratic …
A tale of a principal and many, many agents
In this paper, we investigate a moral hazard problem in finite time with lump-sum and
continuous payments, involving infinitely many agents with mean-field type interactions …
continuous payments, involving infinitely many agents with mean-field type interactions …
Applications of mean field games in financial engineering and economic theory
R Carmona - arXiv preprint arXiv:2012.05237, 2020 - arxiv.org
This is an expanded version of the lecture given at the AMS Short Course on Mean Field
Games, on January 13, 2020 in Denver CO. The assignment was to discuss applications of …
Games, on January 13, 2020 in Denver CO. The assignment was to discuss applications of …
Mean field games of timing and models for bank runs
The goal of the paper is to introduce a set of problems which we call mean field games of
timing. We motivate the formulation by a dynamic model of bank run in a continuous-time …
timing. We motivate the formulation by a dynamic model of bank run in a continuous-time …
Some remarks on mean field games
C Bertucci, JM Lasry, PL Lions - Communications in Partial …, 2019 - Taylor & Francis
In this article, we study three aspects of mean field games (MFG). The first one is the case
when the dynamics of each player depend on the strategies of the other players. The second …
when the dynamics of each player depend on the strategies of the other players. The second …
Deep learning for mean field games and mean field control with applications to finance
R Carmona, M Laurière - arXiv preprint arXiv:2107.04568, 2021 - cambridge.org
Financial markets and more generally macro-economic models involve a large number of
individuals interacting through variables such as prices resulting from the aggregate …
individuals interacting through variables such as prices resulting from the aggregate …
Dynamic programming equation for the mean field optimal stopping problem
We study the optimal stopping problem of McKean–Vlasov diffusions when the criterion is a
function of the law of the stopped process. A remarkable new feature in this setting is that the …
function of the law of the stopped process. A remarkable new feature in this setting is that the …
Monotone solutions for mean field games master equations: finite state space and optimal stopping
C Bertucci - Journal de l'Ecole polytechnique—Mathématiques, 2021 - numdam.org
We present a new notion of solution for mean field games master equations. This notion
allows us to work with solutions which are merely continuous. We first prove results of …
allows us to work with solutions which are merely continuous. We first prove results of …