On the Principle of Smooth Fit for a Class of Singular Stochastic Control Problems for Diffusions
Jin Ma · SIAM Journal on Control and Optimization · 1992
This paper considers the principle of smooth fit for a class of one-dimensional singular stochastic control problems allowing the system to be of nonlinear diffusion type. The existence and the uniqueness of a convex $C^2 $-solution to the corresponding variational inequality are obtained. It is proved that this solution gives the value function of the control problem, and the optimal control process is constructed. As an example of the degenerate case, it is proved that the conclusion is also true for linear systems, and the explicit formula for the smooth fit points is derived.