151 citations · 155 across the 7 of their papers we have counts for
8 papers
Local well-posedness of general mean field game master equations
Chenchen Mou, Jianfeng Zhang, Jianjun Zhou
This paper presents a generic approach for establishing mean field game master equations, applicable whenever the mean field equilibrium can be characterized by a McKean-Vlasov for…
On Information Controls
Zihao Gu, Jianfeng Zhang
In this paper we study an optimization problem in which the control is information, more precisely, the control is a -algebra or a filtration. In a dynamic setting, we establish…
Second-order monotonicity conditions and mean field games with volatility control
Chenchen Mou, Jianfeng Zhang, Jianjun Zhou
In this manuscript we study the well-posedness of the master equations for mean field games with volatility control. This infinite dimensional PDE is nonlinear with respect to both…
Controlled Occupied Processes and Viscosity Solutions
H. Mete Soner, Valentin Tissot-Daguette, Jianfeng Zhang
We consider the optimal control of occupied processes which record all positions of the state process. Dynamic programming yields nonlinear equations on the space of positive measu…
Instability and Efficiency of Non-cooperative Games
Jianfeng Zhang
It is well known that a non-cooperative game may have multiple equilibria. In this paper we consider the efficiency of games, measured by the ratio between the aggregate payoff ove…
Viscosity Solutions for HJB Equations on the Process Space
Jianjun Zhou, Nizar Touzi, Jianfeng Zhang
In this paper we investigate a path dependent optimal control problem on the process space with both drift and volatility controls, with possibly degenerate volatility. The dynamic…
Set-valued Hamilton-Jacobi-Bellman Equations
Melih İşeri, Jianfeng Zhang
Building upon the dynamic programming principle for set-valued functions arising from many applications, in this paper we propose a new notion of set-valued PDEs. The key component…
Dual formulation of second order target problems
H. Mete Soner, Nizar Touzi, Jianfeng Zhang
This paper provides a new formulation of second order stochastic target problems introduced in [SIAM J. Control Optim. 48 (2009) 2344-2365] by modifying the reference probability s…