标题:GENERALIZED HAMILTON-JACOBI-BELLMAN EQUATIONS WITH DIRICHLET BOUNDARY CONDITION AND STOCHASTIC EXIT TIME OPTIMAL CONTROL PROBLEM
作者:Buckdahn, Rainer; Nie, Tianyang
作者机构:[Buckdahn, Rainer] Univ Bretagne Occidentale, Math Lab, F-29285 Brest 3, France.; [Buckdahn, Rainer; Nie, Tianyang] Shandong Univ, Sch Math, Jinan 2 更多
通讯作者:Nie, Tianyang
通讯作者地址:[Nie, TY]Shandong Univ, Sch Math, Jinan 250100, Peoples R China.
来源:SIAM JOURNAL ON CONTROL AND OPTIMIZATION
出版年:2016
卷:54
期:2
页码:602-631
DOI:10.1137/140998160
关键词:stochastic exit time; optimal control; backward stochastic differential; equations; Hamilton-Jacobi-Bellman equations; viscosity solutions
摘要:We consider a kind of stochastic exit time optimal control problem in which the cost functional is defined through a nonlinear backward stochastic differential equation. We study the regularity of the value function for such a control problem. Then, extending Peng's backward semigroup method, we show the dynamic programming principle. Moreover, we prove that the value function is a viscosity solution to the following generalized Hamilton-Jacobi-Bellman equation with Dirichlet boundary condition: inf(v subset of V) {L(x,v)u(x)+f(x,u(x),del u(x)sigma(x,v),v)} = 0, x is an element of D, and u(x) = g(x), x is an element of partial derivative D, where D is a bounded set in R-d, V is a compact set in R-k, and for u is an element of C-2(D) and (x, v) is an element of D x V, L(x,v)u(x) :=1/2 Sigma(d)(i,j=1) (sigma sigma*) i,j (x, v) partial derivative(2)u/partial derivative x(i)partial derivative x(j) (x) Sigma(d)(i=1) b(i)(x, v) partial derivative u/partial derivative x(i) (x).
收录类别:EI;SCOPUS;SCIE
WOS核心被引频次:4
Scopus被引频次:3
资源类型:期刊论文
原文链接:https://www.scopus.com/inward/record.uri?eid=2-s2.0-84964822052&doi=10.1137%2f140998160&partnerID=40&md5=c61fc423bf2e69841377b18d241ab4d0
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