4 papers · 1 filter
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…
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…
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…