ON APPROXIMATIVE SOLUTIONS OF MULTISTOPPING PROBLEMS

• 成果类型: Article
• 署名作者: Faller, Andreas; Rueschendorf, Ludger
• 署名单位: University of Freiburg
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/10-AAP747
• 发表日期: 2011
• 页码: 1965-1993
• 关键词: sequential selection

摘要

In this paper, we consider multistopping problems for finite discrete time sequences X1, ... , X-n. m-stops are allowed and the aim is to maximize the expected value of the best of these m stops. The random variables are neither assumed to be independent not to be identically distributed. The basic assumption is convergence of a related imbedded point process to a continuous time Poisson process in the plane, which serves as a limiting model for the stopping problem. The optimal m-stopping curves for this limiting model are determined by differential equations of first order. A general approximation result is established which ensures convergence of the finite discrete time m-stopping problem to that in the limit model. This allows the construction of approximative solutions of the discrete time m-stopping problem. In detail, the case of i.i.d. sequences with discount and observation costs is discussed and explicit results are obtained.