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Download fileSobolev weak solutions of the Hamilton--Jacobi--Bellman equations
journal contribution
posted on 2016-11-10, 11:05 authored by Lifeng Wei, Zhen Wu, Huaizhong ZhaoThis paper is concerned with the Sobolev weak solutions of the Hamilton-Jacobi-Bellman (HJB) equations. These equations are derived from the dynamic programming principle in the study of stochastic optimal control problems. Adopting the Doob-Meyer decomposition theorem as one of the main tools, we prove that the optimal value function is the unique Sobolev weak solution of the corresponding HJB equation. In the recursive optimal control problem, the cost function is described by the solution of a backward stochastic differential equation (BSDE). This problem has a practical background in economics and finance. We prove that the value function is the unique Sobolev weak solution of the related HJB equation by virtue of the nonlinear Doob-Meyer decomposition theorem introduced in the study of BSDEs.
History
School
- Science
Department
- Mathematical Sciences
Published in
SIAM Journal on Control and OptimizationVolume
52Issue
3Pages
1499 - 1526Citation
WEI, L., WU, Z. and ZHAO, H., 2014. Sobolev weak solutions of the Hamilton Jacobi Bellman equations. SIAM Journal on Control and Optimization, 52 (3), pp. 1499 - 1526Publisher
© Society for Industrial and Applied MathematicsVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Acceptance date
2014-01-29Publication date
2014-05-06Notes
This article was published in the SIAM Journal on Control and Optimization [© SIAM] and the definitive version is available at: http://dx.doi.org/10.1137/120889174ISSN
0363-0129eISSN
1095-7138Publisher version
Language
- en