Stochastic Control and Differential Games with Path-Dependent Influence of Controls on Dynamics and Running Cost

Understand

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.