Sensitivity analysis for HJB equations with an application to coupled backward-forward systems
Analysis of PDEs
2015-07-31 v2
Abstract
In this paper, we analyse Lipschitz continuous dependence of the solution to Hamilton-Jacobi-Bellman equations on a functional parameter. This sensitivity analysis not only has the interest on its own, but also is important for the mean field games methodology, namely for solving a coupled system of backward-forward equations. We show that the unique solution to a Hamilton-Jacobi-Bellman equation and its spacial gradient are Lipschitz continuous uniformly with respect to the functional parameter. In particular, we provide verifiable criteria for the so-called feedback regularity condition. Finally as an application, we show how the sensitive results are used to solved the coupled system of backward-forward equations.
Cite
@article{arxiv.1303.6234,
title = {Sensitivity analysis for HJB equations with an application to coupled backward-forward systems},
author = {Vassili Kolokoltsov and Wei Yang},
journal= {arXiv preprint arXiv:1303.6234},
year = {2015}
}