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摘要翻译：
本文提出了一个非线性随机微分方程(SDE)，它模拟了金融市场中收益的概率密度函数(PDF)和绝对收益的功率谱。绝对收益作为衡量市场波动性的指标，在该模型中被视为一个长期记忆随机变量。SDE是从与先前提出的金融市场交易活动模型的类比中得到的，并在非广泛的统计力学框架内进行了推广。所提出的随机模型利用PDF和功率谱密度两种幂律统计量生成收益率的时间序列，再现了纽约证券交易所一分钟交易收益率的经验数据。
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英文标题：
《A long-range memory stochastic model of the return in financial markets》
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作者：
V. Gontis, J. Ruseckas and A. Kononovicius
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最新提交年份：
2009
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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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英文摘要：
We present a nonlinear stochastic differential equation (SDE) which mimics the probability density function (PDF) of the return and the power spectrum of the absolute return in financial markets. Absolute return as a measure of market volatility is considered in the proposed model as a long-range memory stochastic variable. The SDE is obtained from the analogy with earlier proposed model of trading activity in the financial markets and generalized within the nonextensive statistical mechanics framework. The proposed stochastic model generates time series of the return with two power law statistics, i.e., the PDF and the power spectral density, reproducing the empirical data for the one minute trading return in the NYSE.
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PDF链接：
https://arxiv.org/pdf/0901.0903
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