SOBOLEV WEAK SOLUTIONS OF THE HAMILTON-JACOBI-BELLMAN EQUATIONS

作     者：Wei, Lifeng Wu, Zhen Zhao, Huaizhong 

作者机构：Ocean Univ China Sch Math Sci Qingdao 266003 Peoples R China Shandong Univ Sch Math Jinan 250100 Peoples R China Univ Loughborough Dept Math Sci Loughborough LE11 3TU Leics England 

出 版 物：《SIAM JOURNAL ON CONTROL AND OPTIMIZATION》 (工业与应用数学会控制与最佳化杂志)

年 卷 期：2014年第52卷第3期

页      面：1499-1526页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0811[工学-控制科学与工程] 0701[理学-数学] 

基　　金：Natural Science Foundations of China [11221061, 61174092] 111 Project [B12023] National Science Fund for Distinguished Young Scholars of China 

主　　题：dynamic programming principle Hamilton-Jacobi-Bellman equations Sobolev weak solutions backward stochastic differential equations Doob-Meyer decomposition theorem 

摘      要：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.