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

Vassili Kolokoltsov, Wei Yang

Research output: Working paper

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Abstract

In this paper, we analyse the dependence of the solution of 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 backward-forward system. We show that the unique solution of a Hamilton-Jacobi-Bellman equation and its spacial gradient are Lipschitz continuous uniformly with respect to a functional parameter. In particular, we provide verifiable criteria for the so-called feedback regularity condition.
Original languageEnglish
Place of PublicationIthaca, NY
Number of pages25
Publication statusUnpublished - 2013

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Keywords

  • sensitivity analysis
  • HJB equations
  • backward-forward system
  • Hamilton-Jacobi-Bellman equations
  • functional parameter
  • mean field control
  • feedback regularity

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