Some Results for the Acceptance Urn Model

An urn contains m balls of value -1 and p balls of value +1. The balls are drawn randomly without replacement until the urn is emptied. Before each ball is drawn, the player is asked whether or not she would like to accept the next ball drawn, with the payout being the value of the ball. We present...

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Bibliographic Details
Published in:SIAM journal on discrete mathematics 2010-01, Vol.24 (3), p.876-891
Main Authors: Suen, Stephen, Wagner, Kevin P
Format: Article
Language:English
Subjects:
Acceptance
Bayesian analysis
Mathematical models
Players
Probability
Studies
Upper bounds
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Summary:An urn contains m balls of value -1 and p balls of value +1. The balls are drawn randomly without replacement until the urn is emptied. Before each ball is drawn, the player is asked whether or not she would like to accept the next ball drawn, with the payout being the value of the ball. We present results related to the random version of this (m, p) acceptance urn, where the total number of balls n is known and the number of balls with value +1 is unknown and random. We also consider the ruin problem for the (m, p) urn: The player has b dollars available to play the (m, p) urn and is ruined if at some point she has lost b dollars. We find a necessary condition for ruin, and use this condition to give upper bounds for the ruin probability. We also examine the ruin problem for the random acceptance urn, finding the ruin probability provided the initial distribution satisfies some additional conditions. [PUBLICATION ABSTRACT]
ISSN:0895-4801
1095-7146
DOI:10.1137/090767339