On the smoothness of value functions - Bruno Strulovici; Martin Szydlowski (Northwestern University, Kellogg School of Management, Center for Mathematical Studies in Economics and Management Science, 2012)
We prove that under standard Lipschitz and growth conditions, the value function of all optimal control problems for one-dimensional diffusions is twice differentiable, as long as the control space is compact and the volatility is uniformly bounded below, away from zero. Under similar conditions, the value function of any optimal stopping problem is differentiable.
Keywords: C61; C62; 330; Stochastic Control; Super Contact; Smooth Pasting; Value Function