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题名:	Strong optimality of bold play for discounted Dubins-Savage gambling problems with time-dependent parameters
作者:	姚怡慶;陳美如 Yao, Yi-Ching;Chen, May-Ru
关键词:	Gambling theory;primitive casin;discount facto;optimal strategy
日期:	2008-06
上传时间:	2010-10-19 22:56:05 (UTC+8)
摘要:	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 (the goal) by gambling repeatedly with suitably chosen stakes. This problem has recently been extended in a unifying framework to account for limited playing time as well as future discounting, under which bold play is known to be optimal provided that w ≤ ½ ≤ r. This paper is concerned with a further extension of the Dubins-Savage gambling problem involving time-dependent parameters, and shows that bold play not only maximizes the probability of reaching the goal, but also stochastically minimizes the number of plays needed to reach the goal. As a result, bold play also maximizes the expected utility, where the utility at the goal is only required to be monotone decreasing with respect to the number of plays needed to reach the goal. It is further noted that bold play remains optimal even when the time-dependent parameters are random.
關聯:	Journal of Applied Probability, 45(2), 403-416
数据类型:	article
DOI 連結:	http://dx.doi.org/10.1239/jap/1214950356
DOI:	10.1239/jap/1214950356
显示于类别:	[統計學系] 期刊論文

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