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From the currency rate quotations onto strings and brane world scenarios

机译:从货币汇率报价到弦乐世界

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In the paper, we study the projections of the real exchange rate dynamics onto the string-like topology. Our approach is inspired by the contemporary movements in the string theory. The string map of data is defined here by the boundary conditions, characteristic length, real valued and the method of redistribution of information. As a practical matter, this map represents the detrending and data standardization procedure. We introduced maps onto 1-end-point and 2-end-point open strings that satisfy the Dirichlet and Neumann boundary conditions. The questions of the choice of extra-dimensions, symmetries, duality and ways to the partial compactification are discussed. Subsequently, we pass to higher dimensional and more complex objects. The 2D-Brane was suggested which incorporated bid-ask spreads. Polarization by the spread was considered which admitted analyzing arbitrage opportunities on the market where transaction costs are taken into account. The model of the rotating string which naturally yields calculation of angular momentum is suitable for tracking of several currency pairs. The systematic way which allows one suggest more structured maps suitable for a simultaneous study of several currency pairs was analyzed by means of the Gateaux generalized differential calculus. The effect of the string and brane maps on test data was studied by comparing their mean statistical characteristics. The study revealed notable differences between topologies. We review the dependence on the characteristic string length, mean fluctuations and properties of the intra-string statistics. The study explores the coupling of the string amplitude and volatility. The possible utilizations of the string theory approach in financial markets are slight.
机译:在本文中,我们研究了实际汇率动态对类字符串拓扑的投影。我们的方法受到弦理论中当代运动的启发。数据的字符串映射在此由边界条件,特征长度,实值和信息的重新分配方法定义。实际上,该图表示趋势和数据标准化过程。我们将映射引入满足Dirichlet和Neumann边界条件的1端点和2端点开放字符串上。讨论了尺寸,对称性,对偶性和局部压实方式选择的问题。随后,我们传递到更高维度和更复杂的对象。有人建议将2D-Brane纳入买卖差价。考虑到价差的两极分化,这种分析承认分析了考虑了交易成本的市场上的套利机会。自然产生角动量计算的旋转弦模型适合于跟踪几个货币对。通过使用Gateaux广义微分法,分析了一种系统的方法,该方法允许提出更适合同时研究几种货币对的结构化地图。通过比较字符串和麸皮图的平均统计特性,研究了它们对测试数据的影响。该研究揭示了拓扑之间的显着差异。我们回顾了对特征字符串长度,平均波动和内部字符串统计属性的依赖性。该研究探索了弦幅值和波动率的耦合。字符串理论方法在金融市场中的可能用途很小。

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