摘要翻译：
本文用数值方法研究了实际汇率动力学在类弦拓扑上的投影。我们的方法受到弦理论中当代运动的启发。通过边界条件、特征长度、实值和信息再分配方法定义了数据的字符串映射。作为一个实际问题，这张地图代表了去中心化和数据标准化的过程。在满足Dirichlet和Neumann边界条件的1端点和2端点开弦上引入了映射。讨论了超维数的选择、对称性、对偶性和部分紧致的方法等问题。随后，我们转向更高维和更复杂的对象。2D-Brane被提出，它包含了买卖价差。利差的两极分化被考虑，这允许分析市场上的套利机会，其中考虑了交易成本。旋转弦模型自然产生角动量计算，适用于多种货币对的跟踪。本文用广义微分方法分析了一种系统的方法，它使人们可以提出更多的结构化映射，适合于同时研究几种货币对。通过比较它们的平均统计特性，研究了弦图和膜图对测试数据的影响。这项研究揭示了拓扑结构之间的显著差异。我们回顾了特征字符串长度的依赖性，平均涨落和字符串内统计的性质。研究了弦振幅和波动率的耦合。
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英文标题：
《From the currency rate quotations onto strings and brane world scenarios》
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作者：
D. Horvath, R. Pincak
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最新提交年份：
2011
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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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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 the paper, we study numerically 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 G\^{a}teaux 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.
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PDF链接：
https://arxiv.org/pdf/1104.4716