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June, 1980 Optimal Stopping in an Urn
Wen-chen Chen, Norman Starr
Ann. Probab. 8(3): 451-464 (June, 1980). DOI: 10.1214/aop/1176994720


An urn contains $N$ objects, labelled with the integers $1, \cdots, N$. One object is removed at a time, without replacement. If after $n$ draws the largest number which has been observed is $m_n$, and the process is terminated, we receive a payoff $f(n, m_n)$. For payoff functions $f$ in a certain class, the optimal time to stop is with draw $$\tau_f = \inf\{n \geqslant 0: m_n - n \geqslant j_n\}$$ where the $j_n$ are computable from a simple algorithm, which permits also exact computation of the value $$V_f = E\{f(\tau_f, m_{\tau_f})\}.$$ We also study the behavior of $V_f$ when $N$ is large in special cases.


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Wen-chen Chen. Norman Starr. "Optimal Stopping in an Urn." Ann. Probab. 8 (3) 451 - 464, June, 1980.


Published: June, 1980
First available in Project Euclid: 19 April 2007

zbMATH: 0434.60046
MathSciNet: MR573286
Digital Object Identifier: 10.1214/aop/1176994720

Primary: 62L15
Secondary: 60G40

Keywords: dynamic programming , maximum process , myopic strategy , Optimal stopping , secretary problem , urn sampling

Rights: Copyright © 1980 Institute of Mathematical Statistics

Vol.8 • No. 3 • June, 1980
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