Paper Info
Title
GENERALIZED HAMILTON-JACOBI-BELLMAN EQUATIONS WITH DIRICHLET BOUNDARY CONDITION AND STOCHASTIC EXIT TIME OPTIMAL CONTROL PROBLEM
Abstract
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).
Year
DOI
Venue
2016
10.1137/140998160
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Keywords
Field
DocType
stochastic exit time,optimal control,backward stochastic differential equations,Hamilton-Jacobi-Bellman equations,viscosity solutions
Nabla symbol,Mathematical optimization,Mathematical analysis,Bounded set,Dirichlet boundary condition,Compact space,Bellman equation,Stochastic differential equation,Semigroup,Viscosity solution,Mathematics
Journal
Volume
Issue
ISSN
54
2
0363-0129
Citations 
PageRank 
References 
0
0.34
0
Authors
2
Name
Order
Citations
PageRank
Rainer Buckdahn16218.36
Tianyang Nie210.69