2 citations · 4 across the 9 of their papers we have counts for
10 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…
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…
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…
Fractional Backward Stochastic Partial Differential Equations with Applications to Stochastic Optimal Control of Partially Observed Systems driven by Lévy Processes
Yuyang Ye, Yunzhang Li, Shanjian Tang
In this paper, we study the Cauchy problem for backward stochastic partial differential equations (BSPDEs) involving fractional Laplacian operator. Firstly, by employing the martin…
Viscosity Solutions of Second Order Path-Dependent Partial Differential Equations and Applications
Shanjian Tang, Jianjun Zhou
In this article, a notion of viscosity solutions is introduced for fully nonlinear second order path-dependent partial differential equations in the spirit of [Zhou, Ann. Appl. Pro…
Optimal Control of Unbounded Functional Stochastic Evolution Systems in Hilbert Spaces: Second-Order Path-dependent HJB Equation
Shanjian Tang, Jianjun Zhou
Optimal control and the associated second-order path-dependent Hamilton-Jacobi-Bellman (PHJB) equation are studied for unbounded functional stochastic evolution systems in Hilbert…
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…
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…