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政大機構典藏 > 商學院 > 統計學系 > 期刊論文 > Item 140.119/29045

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/29045

Title:	On Optimality of Bold Play for Discounted Dubins-savage Gambling Problems with Limited Playing Times
Authors:	姚怡慶 Yao, Yi-Ching
Keywords:	Gambling theory;primitive casino;red-and-black;roulette;discount factor;optimal strategy
Date:	2007-09
Issue Date:	2009-06-01 21:34:34 (UTC+8)
Abstract:	In the classic Dubins-Savage subfair primitive casino gambling problem, the gambler can stake any amount in his possession, winning (1 - r)/r times the stake with probability w and losing the stake with probability 1 - w, 0 ≤ w ≤ r ≤ 1. The gambler seeks to maximize the probability of reaching a fixed fortune by gambling repeatedly with suitably chosen stakes. This problem has been extended in several directions to account for limited playing time or future discounting. We propose a unifying framework that covers these extensions, and prove that bold play is optimal provided that w ≤ ½ ≤ r. We also show that this condition is in fact necessary for bold play to be optimal subject to the constraint of limited playing time.
Relation:	Journal of Applied Probability,44,212-225
Data Type:	article
DOI 連結:	http://dx.doi.org/10.1239/jap/1175267173
DOI:	10.1239/jap/1175267173
Appears in Collections:	[統計學系] 期刊論文

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