英文标题：
《Braided and Knotted Stocks in the Stock Market: Anticipating the flash
  crashes》
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作者：
Ovidiu Racorean
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最新提交年份：
2014
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英文摘要：
  A simple and elegant arrangement of stock components of a portfolio (market index-DJIA) in a recent paper [1], has led to the construction of crossing of stocks diagram. The crossing stocks method revealed hidden remarkable algebraic and geometrical aspects of stock market. The present paper continues to uncover new mathematical structures residing from crossings of stocks diagram by introducing topological properties stock market is endowed with. The crossings of stocks are categorized as overcrossings and undercrossings and interpreted as generators of braid that stocks form in the process of prices quotations in the market. Topological structure of the stock market is even richer if the closure of stocks braid is considered, such that it forms a knot. To distinguish the kind of knot that stock market forms, Alexander-Conway polynomial and the Jones polynomials are calculated for some knotted stocks. These invariants of knots are important for the future practical applications topological stock market might have. Such application may account of the relation between Jones polynomial and phase transition statistical models to provide a clear way to anticipate the transition of financial markets to the phase that leads to crisis. The resemblance between braided stocks and logic gates of topological quantum computers could quantum encode the stock market behavior.
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中文摘要：
在最近的一篇论文[1]中，对投资组合（市场指数DJIA）的股票成分进行了简单而优雅的安排，从而构建了股票交叉图。交叉股票法揭示了股票市场隐藏的显著的代数和几何方面。本文通过引入股票市场所具有的拓扑性质，继续揭示股票图交叉处的新数学结构。股票的交叉点分为交叉点和交叉点，并被解释为股票在市场报价过程中形成的辫子的产生者。如果考虑到股票辫子的闭合，股票市场的拓扑结构更加丰富，以至于它形成了一个结。为了区分股票市场形成的纽结类型，计算了一些纽结股票的Alexander Conway多项式和Jones多项式。这些节点不变量对于股票市场可能具有的未来实际应用非常重要。这种应用可以解释琼斯多项式和相变统计模型之间的关系，从而为预测金融市场向导致危机的阶段的过渡提供一种明确的方法。编织股票和拓扑量子计算机逻辑门之间的相似性可以对股票市场行为进行量子编码。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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