With or without replacement? Sampling uncertainty in Shepp's urn scheme. (22nd June 2023)

• Record Type: Journal Article
• Authors: Glover, Kristoffer
• Is Part Of: Journal of applied probability. Volume 60:Number 2(2023)
• Page Start: 661
• Page End: 675
• Publication Date: 2023-06-22
• Subjects: Shepp's urn scheme -- optimal stopping -- Brownian bridges -- parameter uncertainty -- sampling; 60G35 -- 90C39; 519.2
• DOI: 10.1017/jpr.2022.78
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract: We introduce a variant of Shepp's classical urn problem in which the optimal stopper does not know whether sampling from the urn is done with or without replacement. By considering the problem's continuous-time analog, we provide bounds on the value function and, in the case of a balanced urn (with an equal number of each ball type), an explicit solution is found. Surprisingly, the optimal strategy for the balanced urn is the same as in the classical urn problem. However, the expected value upon stopping is lower due to the additional uncertainty present.