摘要翻译：
胖尾分布的大偏差，即那些衰减慢于指数的分布，不仅相对可能发生，而且还以一种相当奇特的方式发生，即整个样本偏差的有限部分集中在单个变量上。大偏差区域与典型涨落区域通过相变而分离，在相变中样品中各点之间的对称性自发地被打破。对于带有厚尾微观噪声的随机过程，这意味着虽然典型的实现由具有连续样本路径的扩散过程很好地描述，但大偏差路径通常是不连续的。对于具有胖尾分布元素的随机矩阵的特征值，在矩阵迹异常大的情况下，大偏差只集中在单个特征值上，而在细尾世界中，大偏差影响整个分布。这些结果很自然地应用于金融领域。由于金融类股票的价格动态具有厚尾增量的特征，股票价格的大幅波动有望通过离散跳跃来实现。有趣的是，我们发现价格的大幅波动更有可能通过连续的漂移而不是不连续的跳跃来实现。事实上，自相关抑制了大偏差的集中。与随机矩阵理论的预测相比，金融协方差矩阵也表现出异常大的特征值，即市场模式。我们表明，这是由一个具有超额协方差的大偏差来解释的，而不是由一个具有超额波动率的大偏差来解释的。
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英文标题：
《On the concentration of large deviations for fat tailed distributions,
  with application to financial data》
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作者：
Mario Filiasi, Giacomo Livan, Matteo Marsili, Maria Peressi, Erik
  Vesselli, Elia Zarinelli
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最新提交年份：
2014
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics        物理学
二级分类：Data Analysis, Statistics and Probability        数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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英文摘要：
  Large deviations for fat tailed distributions, i.e. those that decay slower than exponential, are not only relatively likely, but they also occur in a rather peculiar way where a finite fraction of the whole sample deviation is concentrated on a single variable. The regime of large deviations is separated from the regime of typical fluctuations by a phase transition where the symmetry between the points in the sample is spontaneously broken. For stochastic processes with a fat tailed microscopic noise, this implies that while typical realizations are well described by a diffusion process with continuous sample paths, large deviation paths are typically discontinuous. For eigenvalues of random matrices with fat tailed distributed elements, a large deviation where the trace of the matrix is anomalously large concentrates on just a single eigenvalue, whereas in the thin tailed world the large deviation affects the whole distribution. These results find a natural application to finance. Since the price dynamics of financial stocks is characterized by fat tailed increments, large fluctuations of stock prices are expected to be realized by discrete jumps. Interestingly, we find that large excursions of prices are more likely realized by continuous drifts rather than by discontinuous jumps. Indeed, auto-correlations suppress the concentration of large deviations. Financial covariance matrices also exhibit an anomalously large eigenvalue, the market mode, as compared to the prediction of random matrix theory. We show that this is explained by a large deviation with excess covariance rather than by one with excess volatility.
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PDF链接：
https://arxiv.org/pdf/1201.2817