Stochastic Control and Differential Games with Path-Dependent Influence   of Controls on Dynamics and Running Cost
  In this paper, we consider the functional It\^o calculus framework to find a path-dependent version of the Hamilton-Jacobi-Bellman equation for stochastic control problems that feature dynamics and running cost that depend on the path of the control. We also prove a Dynamic Programming Principle for such problems. We apply our results to path-dependence of the delay type. We further study Stochastic Differential Games in this context. 
Yuri F. Saporito
math.PR math.OC