It has been long that literature in finance focuses mainly on price and return but much less on trading volume, even completely ignoring it. There is no information on supply-demand quantity and trading volume in neoclassical finance models. Contrary to one of the clearest predictions of rational models of investment in a neoclassical paradigm, however, trading volume is very high on the world’s stock market. Here we extend Shi’s price-volume differential equation, propose a notion of trading conditioning, and measure the intensity of market crowd trading conditioning by accumulative trading volume probability in the wave equation in terms of classical and operant conditioning in behavior analysis. Then, we develop three kinds of market crowd trading behavior models according to the equation, and test them using high frequency data in China stock market. It is hardly surprising that we find: 1) market crowd behave coherence in interaction widely and reach agreement on a stationary equilibrium price between momentum and reversal traders; 2) market crowd adapt to stationary equilibrium price by volume probability increase or decrease in interaction between market crowd and environment (or information and events) in an open feedback loop, and keep coherence by conversion between the two types of traders when it jumps and results in an expected return from time to time, the outcome of prior trading action; 3) while significant herd and disposition “anomalies” disappear simultaneously by learning experience in a certain circumstance, other behavioral “anomalies”, for examples, greed and panic, pronounce significantly in decision making. Specifically, a contingency of return reinforcement and punishment, which includes a variety of internal and external causes, produces excessive trading volume. The behavioral annotation on the volume probability suggests key links and the new methods of mathematical finance for quantitative behavioral finance.长期以来，金融的学术文献主要关注价格和回报率，很少考虑甚至完全忽视了交易量。新经典金融模型就没有供需量和交易量的信息。然而，与新经典框架理性投资模型的预计结果不同，交易量在世界的股票市场上是非常大的。我们基于Shi的价-量微分方程，根据行为分析中的经典性和操作性条件反射，提出了交易性条件反射的概念，并且用该方程中的累计交易量概率来计量市场群体交易性条件反射的强度。由该方程，我们得到三种市场群体的交易行为模型，并且用我国股市的高频数据进行实证分析。不难发现：1）市场群体在相互作用的过程中普遍地表现出相互一致的行为特征，趋势和反转交易者之间存在着一个大家都能够接受的稳态均衡价格；2）交易行为有时会导致稳态均衡价格出现跳跃、带来预期收益率，这时，市场群体在开放的反馈环中，通过与环境（或信息和事件）之间的相互作用，由成交量概率的增加或减少来适应该均衡价格的变化，趋势和反转交易者也会通过相互转换保持市场群体行为的相互一致性； 3）尽管在某特定环境下市场群体通过学习实践，羊群和处置行为同时消失了，但是其他行为“异象”，例如贪婪与恐慌，在决策中却表现的十分显著。特别地，收益率强化和惩罚过程，其中包含各种内外因素，导致过度交易量。累计交易量概率的行为诠释为计量行为金融学提供了关键性的纽带作用和数学金融的新方法。

In this paper, we study market crowd psychological behaviors in learning by correlation analysis, using every trading high frequency data in China stock market. We introduce a notion of trading conditioning in terms of operant conditioning in psychology and measure its intensity by accumulative trading volume probability in a time interval in the transaction price-volume probability wave equation that can describe market crowd coherence in their interacted trading behavior. We find that there is, in general, significant positive correlation between the rate of price volatility mean return and the change in the intensity of market crowd trading conditioning. They behave significantly disposition effect in stock selling and herd behavior in stock buying with expectation on return simultaneously. Specifically, “the herd” have significant stronger expectation on price momentum than its reversal. Second, there is also a significant negative correlation between them in a subdivided term; market crowd show buy-and-hold behavior when price rises steadily, and panic selling when it drops abruptly in depth. We explain both the puzzle of more peaked, heavily tailed, and clustered characteristics in return distribution by coherence and that of market crowd behavioral “anomalies” by trading conditioning in a unified transaction price-volume probability wave framework.

To brief a transaction volume-price probability wave equation, a new advance in econophysics; To introduce a notion of trading conditioning for the first time in terms of operant conditioning in psychology; To measure the intensity of market crowd’s trading conditioning by transaction volume probability; To test correlation between the rate of mean return and the change in the intensity of trading conditioning subject to the return, using high frequency data in China stock market; To study market crowd’s learning and psychological behavior by correlation analysis, and explain their behavioral“anomalies”by trading conditioning.

We develop a theoretical trading conditioning model subject to price volatility and return information in terms of market psychological behavior, based on analytical transaction volume-price probability wave distributions in which we use transaction volume probability to describe price volatility uncertainty and intensity. Applying the model to high frequent data test in China stock market, we have main findings as follows: 1) there is, in general, significant positive correlation between the rate of mean return and that of change in trading conditioning intensity; 2) it lacks significance in spite of positive correlation in two time intervals right before and just after bubble crashes; and 3) it shows, particularly, significant negative correlation in a time interval when SSE Composite Index is rising during bull market. Our model and findings can test both disposition effect and herd behavior simultaneously, and explain excessive trading (volume) and other anomalies in stock market.