摘要翻译：
在Shafer和Vovk建立的博弈论概率框架下，我们引入了连续时间资产交易博弈的一个新公式（概率与金融：它只是一个博弈！(2001)Wiley)。在我们的公式中，市场连续移动，但投资者在离散的时间内交易，这可以依赖于市场过去的路径。我们证明了投资者本质上可以强迫资产价格路径的变化指数恰好等于2。我们的证明是基于将高频离散时间博弈嵌入到连续时间博弈中，并使用Kumon，Takemura和Takeuchi(Stoch.anal.appl.26（2008）1161--1180）的贝叶斯策略进行离散时间抛硬币博弈。我们还表明，投资者资本过程中的主要增长部分是由关于资产价格经验波动的Kullback-Leibler信息导出的信息量清楚地描述的。
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英文标题：
《A new formulation of asset trading games in continuous time with
  essential forcing of variation exponent》
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作者：
Kei Takeuchi, Masayuki Kumon, Akimichi Takemura
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最新提交年份：
2010
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Trading and Market Microstructure        交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
  We introduce a new formulation of asset trading games in continuous time in the framework of the game-theoretic probability established by Shafer and Vovk (Probability and Finance: It's Only a Game! (2001) Wiley). In our formulation, the market moves continuously, but an investor trades in discrete times, which can depend on the past path of the market. We prove that an investor can essentially force that the asset price path behaves with the variation exponent exactly equal to two. Our proof is based on embedding high-frequency discrete-time games into the continuous-time game and the use of the Bayesian strategy of Kumon, Takemura and Takeuchi (Stoch. Anal. Appl. 26 (2008) 1161--1180) for discrete-time coin-tossing games. We also show that the main growth part of the investor's capital processes is clearly described by the information quantities, which are derived from the Kullback--Leibler information with respect to the empirical fluctuation of the asset price.
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PDF链接：
https://arxiv.org/pdf/0708.0275