英文标题：
《The geometric phase of stock trading》
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作者：
Claudio Altafini
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最新提交年份：
2016
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英文摘要：
  Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote.
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中文摘要：
几何相位描述了在连续时间动力系统中，根据面积规则，变量（称为相位变量）的位移如何与经历循环运动的其他变量（形状变量）相关。本文的目的是证明离散时间系统也可以存在几何相位，甚至当形状空间中的周期面积为零时。这一原则适用于股票交易。形状空间中的零面积周期表示高频交易者通常执行的交易操作类型（以快速时间尺度进入和退出头寸），而相位变量表示交易者的现金余额。在交易影响股票价格的假设下，即使是零区域循环交易操作也可以在不影响股票报价的情况下诱导几何阶段，即利润或损失。
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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：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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