Uniqueness and comparison properties of the viscosity solution to some singular HJB equations

We study viscosity solutions to a class of HJB equations with singular coefficients near at the boundary: cases with either vanishing, or oscillating, or blowing-up diffusion coefficients are included. Because of proper structural conditions, strong comparison principle holds without assigning spatial boundary data, and unbounded initial data can be handled. The result applies to stochastic models for interest rate, and yields new results concerning Cauchy problems with unbounded coefficients.