English

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