%0 Journal Article
%T On viscosity solution of HJB equations with state constraints and reflection control
%A Anup Biswas
%A Hitoshi Ishii
%A Subhamay Saha
%A Lin Wang
%J Mathematics
%D 2015
%I arXiv
%X Motivated by a control problem of a certain queueing network we consider a control problem where the dynamics is constrained in the nonnegative orthant $\mathbb{R}_+$ of the $d$-dimensional Euclidean space and controlled by the reflections at the faces/boundaries. We define a discounted value function associated to this problem and show that the value function is a viscosity solution to a certain HJB equation in $\mathbb{R}_+$ with nonlinear Neumann type boundary condition. Under certain conditions, we also characterize this value function as the unique solution to this HJB equation.
%U http://arxiv.org/abs/1509.01118v1