8 papers
Optimal Control of Unbounded Stochastic Evolution Systems in Hilbert Spaces
Shanjian Tang, Jianjun Zhou
Optimal control and the associated second-order Hamilton-Jacobi-Bellman (HJB) equation are studied for unbounded stochastic evolution systems in Hilbert spaces. A new notion of vis…
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…
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…
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…
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…
Mean Field Games with Major and Minor Agents: the Limiting Problem and Nash Equilibrium
Ziyu Huang, Shanjian Tang
In this paper, we consider a mean field game (MFG) with a major and minor agents. We first consider the limiting problem and allow the coefficients to vary with the conditional…