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arXiv · 1303.6234

Sensitivity analysis for HJB equations with an application to coupled backward-forward systems

Vassili Kolokoltsov·Wei Yang
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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.

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Vassili Kolokoltsov, Wei Yang. 2013-03-25. Sensitivity analysis for HJB equations with an application to coupled backward-forward systems. https://arxiv.org/abs/1303.6234

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