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

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

2005-05-12

arxiv.org/abs/math/0505241v1

Annals of Applied Probability 2005, Vol. 15, No. 2, 1339-1366

Mathematics

Probability

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

Scientific paper

10.1214/105051605000000034

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.

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