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

• 成果类型: Article
• 署名作者: Dupuis, P; Wang, H
• 署名单位: Brown University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000034
• 发表日期: 2005
• 页码: 1339-1366
• 关键词: one-dimensional diffusions; american; options

摘要

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.