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題名 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
關鍵詞 Gambling theory;primitive casin;discount facto;optimal strategy
日期 2008-06
上傳時間 19-十月-2010 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
資料類型 article
DOI http://dx.doi.org/10.1239/jap/1214950356
dc.creator (作者) 姚怡慶;陳美如zh_TW
dc.creator (作者) Yao, Yi-Ching;Chen, May-Ru-
dc.date (日期) 2008-06-
dc.date.accessioned 19-十月-2010 22:56:05 (UTC+8)-
dc.date.available 19-十月-2010 22:56:05 (UTC+8)-
dc.date.issued (上傳時間) 19-十月-2010 22:56:05 (UTC+8)-
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/47290-
dc.description.abstract (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.-
dc.language zh_TWen
dc.language.iso en_US-
dc.relation (關聯) Journal of Applied Probability, 45(2), 403-416en
dc.subject (關鍵詞) Gambling theory;primitive casin;discount facto;optimal strategy-
dc.title (題名) Strong optimality of bold play for discounted Dubins-Savage gambling problems with time-dependent parametersen
dc.type (資料類型) articleen
dc.identifier.doi (DOI) 10.1239/jap/1214950356en_US
dc.doi.uri (DOI) http://dx.doi.org/10.1239/jap/1214950356en_US