5 citations · 13 across the 16 of their papers we have counts for
19 papers
A Variational Approach to Mean Field Type Control
Alain Bensoussan, Ziyu Huang, Sheung Chi Phillip Yam
Variational methods have been used to study stochastic control for long, see Bensoussan (1982) and Bensoussan-Lions (1978) for the early works. More precisely, variational approach…
On Convergence Rates of General -Player Stackelberg Games to their Mean Field Limits
Alain Bensoussan, Ziyu Huang, Sheng Wang +1
In this article, we establish precise convergence rates of a general class of -Player Stackelberg games to their mean field limits, which allows the response time delay of infor…
Mean Field Type Control Problems Driven by Jump-diffusions
Alain Bensoussan, Ziyu Huang, Shanjian Tang +1
In this article, we apply a probabilistic approach to study general mean field type control (MFTC) problems with jump-diffusions, and give the first global-in-time solution. We all…
Control and optimization for Neural Partial Differential Equations in Supervised Learning
Alain Bensoussan, Minh-Binh Tran, Bangjie Wang
Although there is a substantial body of literature on control and optimization problems for parabolic and hyperbolic systems, the specific problem of controlling and optimizing the…
Second Order Fully Nonlinear Mean Field Games with Degenerate Diffusions
Alain Bensoussan, Ziyu Huang, Shanjian Tang +1
In this article, we study the global-in-time well-posedness of second order mean field games (MFGs) with both nonlinear drift functions simultaneously depending on the state, distr…
Control on Hilbert Space and Mean Field Control: the Common Noise Case
Alain Bensoussan, P. Jameson Graber, Phillip Yam
The objective of this paper is to provide an equivalent of the theory developed in P.~Cardaliaguet, F.~Delarue, J.M.~Lasry, P.L.~Lions \cite{CDLL}, following the approach of contro…
On stochastic control problems with higher-order moments
Yike Wang, Jingzhen Liu, Alain Bensoussan +2
In this paper, we focus on a class of time-inconsistent stochastic control problems, where the objective function includes the mean and several higher-order central moments of the…
On Mean Field Monotonicity Conditions from Control Theoretical Perspective
Alain Bensoussan, Ziyu Huang, Shanjian Tang +1
In this article, from the viewpoint of control theory, we discuss the relationships among the commonly used monotonicity conditions that ensure the well-posedness of the solutions…
A Class of Degenerate Mean Field Games, Associated FBSDEs and Master Equations
Alain Bensoussan, Ziyu Huang, Shanjian Tang +1
In this paper, we study a class of degenerate mean field games (MFGs) with state-distribution dependent and unbounded functional diffusion coefficients. With a probabilistic method…
A Control Theoretical Approach to Mean Field Games and Associated Master Equations
Alain Bensoussan, Ho Man Tai, Tak Kwong Wong +1
We prove the global-in-time well-posedness for a broad class of mean field game problems, which is beyond the special linear-quadratic setting, as long as the mean field sensitivit…
Degenerate Mean Field Type Control with Linear and Unbounded Diffusion, and their Associated Equations
Alain Bensoussan, Ziyu Huang, Shanjian Tang +1
We study the well-posedness of a system of forward-backward stochastic differential equations (FBSDEs) corresponding to a degenerate mean field type control problem, when the diffu…
Global Well-Posedness of First-Order Mean Field Games and Master Equations with Nonlinear Dynamics
Alain Bensoussan, Tak Kwong Wong, Sheung Chi Phillip Yam +1
This article presents the variant of the approach introduced in the recent work of Bensoussan, Wong, Yam and Yuan [13] to the generic first-order mean field game problem. A major c…
Linear Quadratic Extended Mean Field Games and Control Problems
Alain Bensoussan, Bohan Li, Sheung Chi Phillip Yam
We provide a thorough study of a general class of linear-quadratic extended mean field games and control problems in any dimensions where the mean field terms are allowed to be unb…
Maximum Principle for Mean Field Type Control Problems with General Volatility Functions
Alain Bensoussan, Ziyu Huang, Sheung Chi Phillip Yam
In this paper, we study the maximum principle of mean field type control problems when the volatility function depends on the state and its measure and also the control, by using o…
Mathematical formulation of a dynamical system with dry friction subjected to external forces
A. Bensoussan, A. Brouste, F. B. Cartiaux +2
We consider the response of a one-dimensional system with friction. S.W. Shaw (Journal of Sound and Vibration, 1986) introduced the set up of different coefficients for the static…
Existence and uniqueness of solutions for Bertrand and Cournot mean field games
P. Jameson Graber, Alain Bensoussan
We study a system of partial differential equations used to describe Bertrand and Cournot competition among a continuum of producers of an exhaustible resource. By deriving new a p…
Control Problem on Space of Random Variables and Master Equation
Alain Bensoussan, Phillip Yam
We study in this paper a control problem in a space of random variables. We show that its Hamilton Jacobi Bellman equation is related to the Master equation in Mean field theory. P…
Mean Field Games with a Dominating Player
Alain Bensoussan, Michael Chau, Phillip Yam
In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other thro…
An analytic approach to the ergodic theory of stochastic variational inequalities
Alain Bensoussan, Laurent Mertz
In an earlier work made by the first author with J. Turi (Degenerate Dirichlet Problems Related to the Invariant Measure of Elasto-Plastic Oscillators, AMO, 2008), the solution of…