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arXiv 0804.4191q-fin.STphysics.soc-ph
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市场波动理论

Theory of market fluctuations

S. V. Panyukov

摘要:

提出了外部资源再分配的经济增长融合机制。它导致了企业规模的Zipf分布,由于规模依赖效应,转向拉伸指数,并预测个人之间的指数分布的收入。我们还提出了新的方法来描述市场上的波动,热(短时间)和冷(长时间)的自由度的分离的基础上,预测帐篷状分布的波动与稳定的尾部指数μ =3(μ =2的新闻)。该理论预测了可观察到的分布不对称性及其大小依赖性。以金融市场为例,该理论解释了市场的首次磨坊模式、条件分布、D-微笑、Z形响应、条件双动态、偏度等,并推导了Langeven方程组,该方程组预测了价格变动对交易量的对数依赖关系和跳跃后的波动模式。我们计算了不同时间尺度下的价格分布参数、相关函数和赫斯特指数。在很大程度上,价格经历了分数布朗运动与混沌切换的长期持续和反持续的行为,我们计算相应的概率,响应函数,和风险。

英文摘要:

We propose coalescent mechanism of economic grow because of redistribution of external resources. It leads to Zipf distribution of firms over their sizes, turning to stretched exponent because of size-dependent effects, and predicts exponential distribution of income between individuals. We also present new approach to describe fluctuations on the market, based on separation of hot (short-time) and cold (long-time) degrees of freedoms, which predicts tent-like distribution of fluctuations with stable tail exponent mu=3 (mu=2 for news). The theory predicts observable asymmetry of the distribution, and its size dependence. In the case of financial markets the theory explains first time market mill patterns, conditional distribution, D-smile, z-shaped response, conditional double dynamics, the skewness and so on. We derive the set of Langeven equations, which predicts logarithmic dependence of price shift on trading volume and volatility patterns after jumps. We calculate parameters of price distributions, correlation functions and Hurst exponents at different time scales. At large times the price experiences fractional Brownian motion with chaotically switching of long-time persistent and anti-persistent behavior, and we calculate corresponding probabilities, response functions, and risks.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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