6 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 establis…
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…
Set-valued Hamilton-Jacobi-Bellman Equations
Melih Ä°Åeri, 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…
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…
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…