The Annals of Applied Probability

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

Paul Dupuis and Hui Wang

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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 Vh(x), respectively. We identify the rate of convergence of Vh(x) to V(x) and the rate of convergence of the stopping regions, and provide simple formulas for the rate coefficients.

Article information

Source
Ann. Appl. Probab. Volume 15, Number 2 (2005), 1339-1366.

Dates
First available in Project Euclid: 3 May 2005

Permanent link to this document
http://projecteuclid.org/euclid.aoap/1115137977

Digital Object Identifier
doi:10.1214/105051605000000034

Mathematical Reviews number (MathSciNet)
MR2134106

Zentralblatt MATH identifier
02187032

Subjects
Primary: 93E20: Optimal stochastic control 93E35: Stochastic learning and adaptive control 60J55: Local time and additive functionals 90C59: Approximation methods and heuristics

Keywords
Optimal stopping continuous time discrete time diffusion process rate of convergence local time

Citation

Dupuis, Paul; Wang, Hui. On the convergence from discrete to continuous time in an optimal stopping problem. Ann. Appl. Probab. 15 (2005), no. 2, 1339--1366. doi:10.1214/105051605000000034. http://projecteuclid.org/euclid.aoap/1115137977.


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