Linear potential

  • 详情 Security Transaction Volume/Price Probability Wave Equation (证券成交量价的几率波方程)
    In this paper, the author observes a stationary transaction volume distribution over a trading price range in intraday transactions on individual stocks by studying relationship between the volume and price of transaction through amount of transaction in stock market. The transaction or accumulated trading volume gradually emerges kurtosis near the price mean value over a price range when it takes a longer trading time, regardless of actual price fluctuation path, time series, or total transaction volume in the time interval. The volume/price behaves a probability wave toward an equilibrium price, driven by a restoring force that can be represented by a linear potential. In terms of physics, the author derives a time-independent transaction volume/price probability wave equation and gets two sets of analytical transaction volume distribution eigenfunctions over a price range when supply or demand quantity varies. By fitting and testing the functions with intraday real transaction volume distribution over a price range on a considerable number of individual stocks in Shanghai 180 Index, the author shows the existence of relative equilibrium in stock market and demonstrates the model validation at this early stage. It concludes that either General Equilibrium Theory or Price Random Walk Hypothesis is an extreme conditional case in the probability wave model. Thus, the author attempts to offer a unified micro and dynamic probability wave theory on transaction volume/price in financial market. 本文作者通过成交金额研究股票市场中的成交量与价格之间关系时,观察到每只股票全天的成交量(即累计交易量)在交易价格区间有一种平稳的分布关系。随着交易时间的延长,累计交易量在交易价格区间逐渐显现出在成交价格均值附近峰化的分布特征。这一特征与体系在此间交易价格涨落的路径、时间序列或总成交量的大小无关。成交量价的运动表现为能够用线性势表示的中心力的作用下,围绕体系某一均衡价格运动的几率波。由此,作者用物理的方法推导出不显含时间变量的证券成交量价的波动方程并且得到当供求关系变化时,两组解析的成交量随价格变化的分布函数。用该函数与上证180指数中一些股票在全天真实的成交量随价格的分布进行拟合和检验,作者初步证明了在股票市场中存在相对均衡并且验证了该模型的有效性。其结论是:无论一般均衡理论还是价格波动的随机游走假说都是几率波模型在极端条件下的一个特例。这样,作者试图提出一个适用于描述金融市场中统一、微观和动态的成交量价几率波理论。
  • 详情 Security Transaction Differential Equation--A Transaction Volume/Price Probability Wave Mo
    Financial market is a typical complex system because it is an open trading system and behaved by a variety of interacting agents. The consequence of the interaction appears quite complex and nonlinear. Therefore, how to observe this system and find a simplified methodology to describe it is, probably, a key to understand and solve the problem. In this paper, the author observes a stationary transaction volume distribution over a trading price range, studied the relationship between the volume and price of transaction through the amount of it in stock market. The probability of accumulated trading volume (i.e. actual supply/demand quantity or transaction volume) that distributes over a trading price range gradually emerges kurtosis near a transaction price mean value in a transaction body system when it takes a longer trading time, regardless of actual trading price fluctuation path, time series, or total transaction volume in the time interval. The volume and price behaves a probability wave toward an equilibrium price, driven by an actual supply/demand quantity restoring or regressive force that can be represented by a linear potential (an autoregressive item in mathematics). In terms of physics, the author derives a time-independent security transaction probability wave differential equation and obtains an explicit transaction volume distribution function over the price, the distribution of absolute zero-order Bessel eigenfunctions, in a stable transaction body system when its supply and demand quantity is dynamic. By fitting and testing the function with intraday real transaction volume distributions over the price on a considerable number of individual stocks in Shanghai 180 Index, the author demonstrates its validation at this early stage, and attempts to offer a micro and dynamic transaction volume/price (actual supply/demand quantity and price) probability wave theory.