Stochastic Control and Differential Games with Path-Dependent Influence of Controls on Dynamics and Running Cost
Probability
2019-02-11 v4 Optimization and Control
Abstract
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.
Keywords
Cite
@article{arxiv.1611.00589,
title = {Stochastic Control and Differential Games with Path-Dependent Influence of Controls on Dynamics and Running Cost},
author = {Yuri F. Saporito},
journal= {arXiv preprint arXiv:1611.00589},
year = {2019}
}
Comments
15 pages, 3 figures