英文标题：
《The Quotient of Normal Random Variables And Application to Asset Price
  Fat Tails》
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作者：
Carey Caginalp and Gunduz Caginalp
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最新提交年份：
2018
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英文摘要：
  The quotient of random variables with normal distributions is examined and proven to have have power law decay, with density $f\\left( x\\right) \\simeq f_{0}x^{-2}$, with the coefficient depending on the means and variances of the numerator and denominator and their correlation. We also obtain the conditional probability densities for each of the four quadrants given by the signs of the numerator and denominator for arbitrary correlation $\\rho \\in\\lbrack-1,1).$ For $\\rho=-1$ we obtain a particularly simple closed form solution for all $x\\in$ $\\mathbb{R}$. The results are applied to a basic issue in economics and finance, namely the density of relative price changes. Classical finance stipulates a normal distribution of relative price changes, though empirical studies suggest a power law at the tail end. By considering the supply and demand in a basic price change model, we prove that the relative price change has density that decays with an $x^{-2}$ power law. Various parameter limits are established.
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中文摘要：
检验并证明正态分布随机变量的商具有幂律衰减，密度为$f\\left（x\\right）\\simeq f\\u0}x ^{-2}$，系数取决于分子和分母的均值和方差及其相关性。我们还获得了四个象限中每个象限的条件概率密度，这些象限由任意相关性的分子和分母的符号给出对于$\\rho=-1$，我们为$$\\mathbb{R}$中的所有$x\\获得了一个特别简单的闭式解。这些结果被应用于经济学和金融学的一个基本问题，即相对价格变化的密度。经典金融学规定了相对价格变化的正态分布，尽管实证研究表明尾部存在幂律。通过考虑基本价格变化模型中的供给和需求，我们证明了相对价格变化具有密度，密度随x ^{-2}$幂律衰减。建立了各种参数限制。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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