English

Viscosity Solutions to First Order Path-Dependent HJB Equations

Analysis of PDEs 2020-09-11 v2 Optimization and Control

Abstract

In this article, a notion of viscosity solutions is introduced for first order path-dependent Hamilton-Jacobi-Bellman (HJB) equations associated with optimal control problems for path-dependent differential equations. We identify the value functional of the optimal control problems as a unique viscosity solution to the associated HJB equations. We also show that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions, and satisfies a stability property.

Keywords

Cite

@article{arxiv.2004.02095,
  title  = {Viscosity Solutions to First Order Path-Dependent HJB Equations},
  author = {Jianjun Zhou},
  journal= {arXiv preprint arXiv:2004.02095},
  year   = {2020}
}

Comments

25 pages

R2 v1 2026-06-23T14:39:38.153Z