In this talk, we explore a two-dimensional parabolic Hamilton–Jacobi–Bellman (HJB) equation constrained by two gradient conditions, arising from a firm’s finite-horizon reversible investment problem. The underlying economic dynamics follow the CEV model (or similar diffusions), which causes the differential operator of the HJB equation to exhibit degeneracy and singularity at zero. We establish regularity results and demonstrate the smoothness of the two free boundaries associated with the HJB equation. Finally, by connecting singular control with a family of switching controls through the solution of a double obstacle problem, we construct the solution to the original HJB equation, which characterizes the firm’s optimal strategy.