Implications of contrarian and one-sided strategies for the fair-coin game

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:118

Article

Horikoshi, Yasunori¹  Takemura, Akimichi¹ 

[1] Univ Tokyo, Grad Sch Informat Sci & Technol, Dept Math Informat, Tokyo 1138654, Japan

关键词: Game-theoretic probability;    Law of the iterated logarithm;    Momentum strategy;    Strong law of large numbers;   

DOI  :  10.1016/j.spa.2007.11.007

来源: Elsevier

【 摘 要 】

We derive some results on contrarian and one-sided strategies of Skeptic for the fair-coin game in the framework of the game-theoretic probability of Shafer and Vovk [G. Shafer and V. Vovk. Probability and Finance - It's Only a Game!, Wiley, New York, 2001]. In particular, as regards the rate of convergence of the strong jaw of large numbers (SLLN), we prove that Skeptic can force that the convergence has to be slower than or equal to O(n(-1/2)). This is achieved by a very simple contrarian strategy of Skeptic. This type of result, bounding the rate of convergence from below, contrasts with more standard results of bounding the rate of SLLN from above by using momentum strategies. We also derive a corresponding one-sided result. (C) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

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