摘要翻译：
本文建立了Dubins和Schwarz关于连续鞅通过时间变化约化为布朗运动的著名结果的非随机模拟。在不作任何随机假设的情况下，我们考虑了一个具有连续价格路径的理想化金融证券。研究表明，典型的价格路径具有二次变异，其中“典型”可以理解为以下博弈论意义：如果二次变异过程不存在，则存在一个交易策略，该交易策略在不冒一个以上货币单位的风险的情况下赚取无限资本。用二次变化过程代替时间，我们证明价格路径变成布朗运动。这与Dubins-Schwarz结果中的结论本质上是相同的，只是概率（构成Wiener测度）是出现的，而不是假定的。在Peter McCullagh未发表的著作的启发下，我们还用博弈论概率论对这一结果给出了一个优雅的陈述。
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英文标题：
《Continuous-time trading and the emergence of probability》
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作者：
Vladimir Vovk
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最新提交年份：
2015
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分类信息：

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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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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英文摘要：
  This paper establishes a non-stochastic analogue of the celebrated result by Dubins and Schwarz about reduction of continuous martingales to Brownian motion via time change. We consider an idealized financial security with continuous price path, without making any stochastic assumptions. It is shown that typical price paths possess quadratic variation, where "typical" is understood in the following game-theoretic sense: there exists a trading strategy that earns infinite capital without risking more than one monetary unit if the process of quadratic variation does not exist. Replacing time by the quadratic variation process, we show that the price path becomes Brownian motion. This is essentially the same conclusion as in the Dubins-Schwarz result, except that the probabilities (constituting the Wiener measure) emerge instead of being postulated. We also give an elegant statement, inspired by Peter McCullagh's unpublished work, of this result in terms of game-theoretic probability theory.
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PDF链接：
https://arxiv.org/pdf/0904.4364