An Optimal Acceptance Policy for an Urn Scheme

Loading...
Thumbnail Image
Penn collection
Statistics Papers
Degree type
Discipline
Subject
optimal stopping
acceptance policy
urn models
Bayesian approach
Discrete Mathematics and Combinatorics
Statistics and Probability
Funder
Grant number
License
Copyright date
Distributor
Related resources
Author
Chen, Robert W
Zame, Alan
Odlyzko, Andrew M
Shepp, Larry A
Contributor
Abstract

An urn contains m balls of value -1 and p balls of value +1. At each turn a ball is drawn randomly, without replacement, and the player decides before the draw whether or not to accept the ball, i.e., the bet where the payoff is the value of the ball. The process continues until all m+p balls are drawn. Let V(m,p) denote the value of this acceptance (m,p) urn problem under an optimal acceptance policy. In this paper, we first derive an exact closed form for V(m,p) and then study its properties and asymptotic behavior. We also compare this acceptance (m,p) urn problem with the original (m,p) urn problem which was introduced by Shepp [Ann. Math. Statist., 40 (1969), pp. 993--1010]. Finally, we briefly discuss some applications of this acceptance (m,p) urn problem and introduce a Bayesian approach to this optimal stopping problem. Some numerical illustrations are also provided.

Advisor
Date Range for Data Collection (Start Date)
Date Range for Data Collection (End Date)
Digital Object Identifier
Series name and number
Publication date
1998-05-01
Journal title
SIAM Journal on Discrete Mathematics
Volume number
Issue number
Publisher
Publisher DOI
Journal Issue
Comments
Recommended citation
Collection