英文标题：
《Complex market dynamics in the light of random matrix theory》
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作者：
Hirdesh K. Pharasi, Kiran Sharma, Anirban Chakraborti and Thomas H.
Seligman
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最新提交年份：
2018
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英文摘要：
We present a brief overview of random matrix theory (RMT) with the objectives of highlighting the computational results and applications in financial markets as complex systems. An oft-encountered problem in computational finance is the choice of an appropriate epoch over which the empirical cross-correlation return matrix is computed. A long epoch would smoothen the fluctuations in the return time series and suffers from non-stationarity, whereas a short epoch results in noisy fluctuations in the return time series and the correlation matrices turn out to be highly singular. An effective method to tackle this issue is the use of the power mapping, where a non-linear distortion is applied to a short epoch correlation matrix. The value of distortion parameter controls the noise-suppression. The distortion also removes the degeneracy of zero eigenvalues. Depending on the correlation structures, interesting properties of the eigenvalue spectra are found. We simulate different correlated Wishart matrices to compare the results with empirical return matrices computed using the S&P 500 (USA) market data for the period 1985-2016. We also briefly review two recent applications of RMT in financial stock markets: (i) Identification of \"market states\" and long-term precursor to a critical state; (ii) Characterization of catastrophic instabilities (market crashes).
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中文摘要：
我们简要概述了随机矩阵理论（RMT），目的是突出计算结果和金融市场作为复杂系统的应用。计算金融学中经常遇到的一个问题是选择一个合适的时期来计算经验互相关回报矩阵。长历元会平滑回归时间序列中的波动，并具有非平稳性，而短历元会导致回归时间序列中的噪声波动，相关矩阵具有高度奇异性。解决这一问题的有效方法是使用功率映射，其中非线性失真应用于短历元相关矩阵。失真参数的值控制噪声抑制。失真还消除了零特征值的退化性。根据相关结构，发现了本征值谱的有趣性质。我们模拟不同的相关Wishart矩阵，将结果与使用1985-2016年期间标准普尔500（美国）市场数据计算的经验回报矩阵进行比较。我们还简要回顾了RMT在金融股票市场中的两个最新应用：（i）识别“市场状态”和临界状态的长期前兆；（ii）灾难性不稳定性的表征（市场崩溃）。
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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：Physics 物理学
二级分类：Physics and Society 物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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