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

Vassili Kolokoltsov, Wei Yang

Research output: Working paper

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.
LanguageEnglish
Place of PublicationIthaca, NY
Number of pages25
Publication statusUnpublished - 2013

Fingerprint

HJB Equation
Hamilton-Jacobi-Bellman Equation
Sensitivity analysis
Sensitivity Analysis
Feedback
Uniformly continuous
Regularity Conditions
Unique Solution
Mean Field
Lipschitz
Game
Gradient
Methodology

Keywords

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

Cite this

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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.",
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Sensitivity analysis for HJB equations with an application to a coupled backward-forward system. / Kolokoltsov, Vassili; Yang, Wei.

Ithaca, NY, 2013.

Research output: Working paper

TY - UNPB

T1 - Sensitivity analysis for HJB equations with an application to a coupled backward-forward system

AU - Kolokoltsov, Vassili

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PY - 2013

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N2 - 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.

AB - 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.

KW - sensitivity analysis

KW - HJB equations

KW - backward-forward system

KW - Hamilton-Jacobi-Bellman equations

KW - functional parameter

KW - mean field control

KW - feedback regularity

UR - http://arxiv.org/abs/1303.6234

M3 - Working paper

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

CY - Ithaca, NY

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