摘要翻译：
在这篇文章中，我们给出了任何受IT过程控制的市场模型的套利的最一般的度量。我们证明了我们的套利测度在num{e}raire和等价概率变化下是不变的。此外，这种测量具有作为规范连接的几何解释。连接具有零曲率当且仅当没有套利。我们证明了鞅定价定理在套利情形下的一个推广。在我们的情况下，任何交易资产的现值都是通过对未来现金流的预期用规范连接的线积分折现而得到的。我们开发了简单的策略来衡量套利使用模拟和真实的市场数据。我们发现，在我们有限的数据样本中，市场在一天或更长的时间范围内是有效的。然而，我们为高频日内数据中的非零套利提供了强有力的证据。这样的事件似乎有一分钟量级的衰减时间。
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英文标题：
《Gauge Invariance, Geometry and Arbitrage》
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作者：
Samuel E. Vazquez, Simone Farinelli
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最新提交年份：
2009
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
  In this work, we identify the most general measure of arbitrage for any market model governed by It\^o processes. We show that our arbitrage measure is invariant under changes of num\'{e}raire and equivalent probability. Moreover, such measure has a geometrical interpretation as a gauge connection. The connection has zero curvature if and only if there is no arbitrage. We prove an extension of the Martingale pricing theorem in the case of arbitrage. In our case, the present value of any traded asset is given by the expectation of future cash-flows discounted by a line integral of the gauge connection. We develop simple strategies to measure arbitrage using both simulated and real market data. We find that, within our limited data sample, the market is efficient at time horizons of one day or longer. However, we provide strong evidence for non-zero arbitrage in high frequency intraday data. Such events seem to have a decay time of the order of one minute.
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PDF链接：
https://arxiv.org/pdf/0908.3043