On the convergence from discrete to continuous time in an optimal stopping problem

Abstract

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

Published at http://dx.doi.org/10.1214/105051605000000034 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)