英文标题：
《On financial applications of the two-parameter Poisson-Dirichlet
distribution》
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作者：
Sergey Sosnovskiy
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最新提交年份：
2015
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英文摘要：
Capital distribution curve is defined as log-log plot of normalized stock capitalizations ranked in descending order. The curve displays remarkable stability over periods of time. Theory of exchangeable distributions on set partitions, developed for purposes of mathematical genetics and recently applied in non-parametric Bayesian statistics, provides probabilistic-combinatorial approach for analysis and modeling of the capital distribution curve. Framework of the two-parameter Poisson-Dirichlet distribution contains rich set of methods and tools, including infinite-dimensional diffusion process. The purpose of this note is to introduce framework of exchangeable distributions on partitions in the financial context. In particular, it is shown that averaged samples from the Poisson-Dirichlet distribution provide approximation to the capital distribution curves in equity markets. This suggests that the two-parameter model can be employed for modelling evolution of market weights and prices fluctuating in stochastic equilibrium.
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中文摘要：
资本分布曲线定义为按降序排列的规范化股票资本化的对数-对数图。曲线在一段时间内表现出显著的稳定性。集合分割上的可交换分布理论是为数学遗传学的目的而发展起来的，最近应用于非参数贝叶斯统计，为资本分布曲线的分析和建模提供了概率组合方法。双参数Poisson-Dirichlet分布的框架包含了丰富的方法和工具，包括无限维扩散过程。本说明的目的是介绍金融环境下分区上可交换分配的框架。特别是，泊松-狄利克雷分布的平均样本提供了股票市场中资本分布曲线的近似值。这表明，双参数模型可用于建模随机均衡中市场权重和价格波动的演变。
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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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