摘要翻译：
最近，Mike和Farmer基于纯订单驱动的市场中订单投放和取消的经验规律，构造了一个非常强大和现实的行为模型来模拟股票价格形成的动态过程，它不仅成功地再现了众所周知的幂律尾巴，而且还再现了其他几个重要的程式化事实。Mike-Farmer模型有三个关键因素：以Hurst指数$H_S$为特征的订单符号的长记忆性，以学生分布（或Tsallis的$Q$-高斯分布）描述的相对订单价格相对于相同最佳价格的分布$X$以及订单取消的动态性。结果表明，不同的Hurst指数$H_s$和学生分布的自由度$\alpha_x$在不同尾指数$\alpha_r$的返回分布$f(r)$中总是产生幂律尾。本文通过对$F(x)$的左部$F_l(x)$和右部$F_r(x)$的不同组合的大量模拟，研究了MF模型中收益分布$F(r)$的幂律尾的来源。我们发现，无论$F_l(x)$是否有幂律尾，只有当$F_l(x)$有幂律尾时才会出现幂律尾。另外，我们发现在不同时间尺度下的MF模型中收益的分布可以很好地用学生分布来模拟，其尾部指数接近于众所周知的立方律，并且随时间尺度的增加而增加。
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英文标题：
《On the probability distribution of stock returns in the Mike-Farmer
  model》
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作者：
Gao-Feng Gu (ECUST), Wei-Xing Zhou (ECUST)
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最新提交年份：
2008
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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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英文摘要：
  Recently, Mike and Farmer have constructed a very powerful and realistic behavioral model to mimick the dynamic process of stock price formation based on the empirical regularities of order placement and cancelation in a purely order-driven market, which can successfully reproduce the whole distribution of returns, not only the well-known power-law tails, together with several other important stylized facts. There are three key ingredients in the Mike-Farmer (MF) model: the long memory of order signs characterized by the Hurst index $H_s$, the distribution of relative order prices $x$ in reference to the same best price described by a Student distribution (or Tsallis' $q$-Gaussian), and the dynamics of order cancelation. They showed that different values of the Hurst index $H_s$ and the freedom degree $\alpha_x$ of the Student distribution can always produce power-law tails in the return distribution $f(r)$ with different tail exponent $\alpha_r$. In this paper, we study the origin of the power-law tails of the return distribution $f(r)$ in the MF model, based on extensive simulations with different combinations of the left part $f_L(x)$ for $x<0$ and the right part $f_R(x)$ for $x>0$ of $f(x)$. We find that power-law tails appear only when $f_L(x)$ has a power-law tail, no matter $f_R(x)$ has a power-law tail or not. In addition, we find that the distributions of returns in the MF model at different timescales can be well modeled by the Student distributions, whose tail exponents are close to the well-known cubic law and increase with the timescale.
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PDF链接：
https://arxiv.org/pdf/0805.3593