Viscosity Solutions to Second Order Path-Dependent Hamilton-Jacobi-Bellman Equations and Applications
Optimization and Control
2022-12-26 v3 Probability
Abstract
In this article, a notion of viscosity solutions is introduced for second order path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with optimal control problems for path-dependent stochastic differential equations. We identify the value functional of optimal control problems as unique viscosity solution to the associated PHJB equations. We also show that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions, and satisfies a stability property. Applications to backward stochastic Hamilton-Jacobi-Bellman equations are also given.
Cite
@article{arxiv.2005.05309,
title = {Viscosity Solutions to Second Order Path-Dependent Hamilton-Jacobi-Bellman Equations and Applications},
author = {Jianjun Zhou},
journal= {arXiv preprint arXiv:2005.05309},
year = {2022}
}
Comments
48 pages. arXiv admin note: text overlap with arXiv:2004.02095, arXiv:1611.05533