英文标题：
《Estimating the Algorithmic Complexity of Stock Markets》
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作者：
Olivier Brandouy, Jean-Paul Delahaye, Lin Ma
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最新提交年份：
2015
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英文摘要：
Randomness and regularities in Finance are usually treated in probabilistic terms. In this paper, we develop a completely different approach in using a non-probabilistic framework based on the algorithmic information theory initially developed by Kolmogorov (1965). We present some elements of this theory and show why it is particularly relevant to Finance, and potentially to other sub-fields of Economics as well. We develop a generic method to estimate the Kolmogorov complexity of numeric series. This approach is based on an iterative \"regularity erasing procedure\" implemented to use lossless compression algorithms on financial data. Examples are provided with both simulated and real-world financial time series. The contributions of this article are twofold. The first one is methodological : we show that some structural regularities, invisible with classical statistical tests, can be detected by this algorithmic method. The second one consists in illustrations on the daily Dow-Jones Index suggesting that beyond several well-known regularities, hidden structure may in this index remain to be identified.
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中文摘要：
金融中的随机性和规律性通常用概率的术语来处理。在本文中，我们基于Kolmogorov（1965）最初开发的算法信息理论，开发了一种完全不同的方法来使用非概率框架。我们介绍了这一理论的一些要素，并说明了为什么它与金融特别相关，也可能与经济学的其他子领域相关。我们发展了一种通用的方法来估计数值序列的Kolmogorov复杂性。该方法基于一个迭代的“规则擦除过程”，该过程用于对金融数据使用无损压缩算法。模拟和真实世界的金融时间序列都提供了示例。本文的贡献有两个方面。第一个是方法论：我们证明了一些经典统计检验所看不见的结构规律，可以通过这种算法方法检测出来。第二个是每日道琼斯指数上的插图，表明除了几个众所周知的规律外，该指数中隐藏的结构可能仍有待确定。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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