Exact probability distribution function for multifractal random walk models of stocks

Exact probability distribution function for multifractal random walk models of stocks
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股票多重分形随机游走模型的精确概率分布函数

DOI：
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发表时间：
2011
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通讯作者：
Z. Struzik
Z. Struzik
中科院分区：
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文献类型：
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作者：
D. Saakian;A. Martirosyan;Chin;Z. Struzik

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我们研究多重分形随机游走（MRW）模型，流行的股票波动在金融市场的建模。精确的概率分布函数（PDF）是通过采用弦理论中推导相关函数的方法推导出来的，包括Selberg积分的分析扩展。我们证明了Y. V. Fyodorov，P. Le Doussal和A.罗索得到的对数随机能量模型（REM）模型是足够的推导出精确的公式的对数收益率的PDF在MRW模型。
We investigate the multifractal random walk (MRW) model, popular in the modelling of stock fluctuations in the financial market. The exact probability distribution function (PDF) is derived by employing methods proposed in the derivation of correlation functions in string theory, including the analytical extension of Selberg integrals. We show that the recent results by Y. V. Fyodorov, P. Le Doussal and A. Rosso obtained with the logarithmic Random Energy Model (REM) model are sufficient to derive exact formulas for the PDF of the log returns in the MRW model.