Solving optimal stopping problems of linear diffusions by applying convolution approximations

We study how the convolution approximation of continuous mappings can be applied in solving optimal stopping problems of linear diffusions whenever the underlying payoff is not differentiable and the smooth fit principle does not necessarily apply. We construct a sequence of smooth reward functions converging uniformly on compacts to the original reward and, consequently, we derive a sequence of continuously differentiable (i.e. satisfying the smooth fit principle) value functions converging to the value of the original stopping problem.