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Title: Sobolev weak solutions of the Hamilton Jacobi Bellman equations
Authors: Wei, Lifeng
Wu, Zhen
Zhao, Huaizhong
Issue Date: 2014
Publisher: © Society for Industrial and Applied Mathematics
Citation: 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 - 1526
Abstract: This 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.
Description: This article was published in the SIAM Journal on Control and Optimization [© SIAM] and the definitive version is available at: http://dx.doi.org/10.1137/120889174
Version: Accepted for publication
DOI: 10.1137/120889174
URI: https://dspace.lboro.ac.uk/2134/23113
Publisher Link: http://dx.doi.org/10.1137/120889174
ISSN: 0363-0129
Appears in Collections:Published Articles (Maths)

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