The aim of this paper is to construct and analyze explicit solutions to a class of Hamilton-Jacobi-Bellman equations with range bounds on the optimal response variable. We construct a fully nonlinear  partial differential equation as a model for the evolution of the risk preference in the optimal investment problem under the random risk process . We construct monotone risk-seeking and risk-averse traveling wave solutions  .
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 .
D
explicit
R
We construct
Using the Riccati transformation we derive and analyze
A
parabolic
R
as a model for the evolution of the risk preference in the optimal investment problem under the random risk process
for the optimal response function
D
risk-seeking and risk-averse
A
and identify parametric regions for which the traveling wave solution has a positive or negative wave speed