A random version of shepp's urn scheme

doi:10.1137/S0895480102418099

淡江大學機構典藏 > 理學院 > 應用數學與數據科學學系 > 期刊論文 > Item 987654321/41295

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Title:	A random version of shepp's urn scheme
Authors:	Chen, Robert W.;Zame, Alan;林千代;Lin, Chien-tai;吳秀芬;Wu, Hsiu-fen
Contributors:	淡江大學數學學系
Keywords:	urn scheme;optimal drawing policy;random coin tossing process;stopping time;the “k” in the hole policy
Date:	2005-06
Issue Date:	2010-01-28 07:12:59 (UTC+8)
Publisher:	Philadelphia: Society for Industrial and Applied Mathematics (SIAM)
Abstract:	In this paper, we consider the following random version of Shepp’s urn scheme: A player is given an urn with n balls. p of these balls have value +1 and n − p have value −1. The player is allowed to draw balls randomly, without replacement, until he or she wants to stop. The player knows n, the total number of balls, but knows only that p, the number of balls of value +1, is a number selected randomly from the set {0,1,2,...,n}. The player wishes to maximize the expected value of the sum of the balls drawn. We ﬁrst derive the player’s optimal drawing policy and an algorithm to compute the player’s expected value at the stopping time when he or she uses the optimal drawing policy. Since the optimal drawing policy is rather intricate and the computation of the player’s optimal expected value is quite cumbersome, we present a very simple drawing policy, which is asymptotically optimal. We also show that this random urn scheme is equivalent to a random coin tossing problem.
Relation:	Siam Journal on Discrete Mathematics 19(1), pp.149-164
DOI:	10.1137/S0895480102418099
Appears in Collections:	[應用數學與數據科學學系] 期刊論文

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