On traveling wave solutions to Hamilton-Jacobi-Bellman equation with   inequality constraints
  The aim of this paper is to construct and analyze solutions to a class of Hamilton-Jacobi-Bellman equations with range bounds on the optimal response variable. Using the Riccati transformation we derive and analyze a fully nonlinear parabolic partial differential equation for the optimal response function. We construct monotone traveling wave solutions and identify parametric regions for which the traveling wave solution has a positive or negative wave speed. 
Naoyuki Ishimura and Daniel Sevcovic
q-fin.PM math.AP