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

Abstract

In this paper, we consider the functional Itô 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.

15 pages, 3 figures

References in corpus (2)

• Functional Itô calculus and stochastic integral representation of martingales
• Systemic Risk and Stochastic Games with Delay