Sum the odds to one and stop

• 成果类型: Article
• 署名作者: Bruss, FT
• 署名单位: Universite Libre de Bruxelles
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1019160340
• 发表日期: 2000
• 页码: 1384-1391
• 关键词: infinite secretary problem

摘要

The objective of this paper is to present two theorems which are directly applicable to optimal stopping problems involving independent indicator functions. The proofs are elementary. One implication of the results is a convenient solution algorithm to obtain the optimal stopping rule and the value. We will apply it to several examples of sequences of independent indicators, including sequences of random length. Another interesting implication of the results is that the in well-known asymptotic value 1/e for the classical best-choice problem is in fact a typical lower bound in a much more general class of problems.