On the Convergence from Discrete to Continuous Time in an Optimal Stopping Problem∗

We consider the problem of optimal stopping for a one dimensional diffusion process. Two classes of admissible stopping times are considered. The Þrst class consists of all non-anticipating stopping times that take values in [0,∞], while the second class further restricts the set of allowed values to the discrete grid {nh : n = 0, 1, 2, · · · ,∞} for some parameter h > 0. The value functions for the two problems are denoted by V (x) and V (x), respectively. We identify the rate of convergence of V (x) to V (x) and the rate of convergence of the stopping regions, and provide simple formulas for the rate coefficients.