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

2005/05/12 by Paul Dupuis, Hui Wang
Mathematics · #math.PR #msc:93E20 #msc:93E35 #msc:60J55 #msc:90C59.

paper · pdf · doi:10.1214/105051605000000034

published as Annals of Applied Probability 2005, Vol. 15, No. 2, 1339-1366 · 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)

arxiv created 2005/05/12 · arxiv updated 2009/12/01

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,∞], 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^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.

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