It has been long that literature in financial academics focuses mainly on price and return but much less on trading volume. In the past twenty years, it has already linked both price and trading volume to economic fundamentals, and explored the behavioral implications of trading volume such as investor’s attitude toward risks, overconfidence, disagreement, and attention etc. However, what is surprising is how little we really know about trading volume. Here we show that trading volume probability represents the frequency of market crowd’s trading action in terms of behavior analysis, and test two adaptive hypotheses relevant to the volume uncertainty associated with price in China stock market. The empirical work reveals that market crowd trade a stock in efficient adaptation except for simple heuristics, gradually tend to achieve agreement on an outcome or an asset price widely on a trading day, and generate such a stationary equilibrium price very often in interaction and competition among themselves no matter whether it is highly overestimated or underestimated. This suggests that asset prices include not only a fundamental value but also private information, speculative, sentiment, attention, gamble, and entertainment values etc. Moreover, market crowd adapt to gain and loss by trading volume increase or decrease significantly in interaction with environment in any two consecutive trading days. Our results demonstrate how interaction between information and news, the trading action, and return outcomes in the three-term feedback loop produces excessive trading volume which includes various internal and external causes. Finally, we reconcile market dynamics and crowd’s trading behaviors in a unified framework by Shi’s price-volume differential equation in stock market where, we assume, investors derive a liquidity utility expressed in terms of trading wealth which is equal to the sum of a probability weighting utility and a reversal utility in reference to an outcome. JEL Classifications: G12, G02, D83 （长期以来，金融学术领域里的文献只注重价格和收益率，却较少研究交易量。在最近的二十年里，金融学术文献已经开始研究价格和交易量两者与经济基本量之间的相互关系，并且探讨交易量的行为内涵，例如投资者对风险的态度、过度自信、不同观点以及关注程度等等。然而，我们还是对交易量的认识知之甚少。本文根据行为分析，用交易量概率来表示市场群体的交易频率，并且通过我国股市来实证检验涉及交易量与价格之间不确定关系的两种适应性假说。实证结果表明：市场群体在每日交易的时间窗口内除了采用简单的经验法则之外，同时还采用有效的适应性方式来从事股票交易，并且逐步倾向于形成一个结果和认同的资产价格；无论该资产价格是否明显地被高估或低估，市场群体在相互作用和竞争的过程中往往能够形成这样一个稳态的均衡价格。这表明了资产价格不仅包含了基本价值同时还包含了非公开信息、投机、情绪、关注、赌博和娱乐等价值。此外，在任意两个连续交易日之间，市场群体在与市场环境的相互作用过程中，通过交易量的增加或减少来有效地适应盈亏。我们的研究结果说明了在由信息、交易与收益结果三项构成的反馈环中，它们之间的相互作用是如何导致了过度交易的，这其中包含了导致过度交易的各种内外因素。最后，我们假设股票市场中的投资者是通过交易财富来产生流动性效用，它等于概率加权效用与相对于结果为参照系的反转效用之和，从而推导出Shi氏价-量微分方程，将市场动力学行为与群体交易行为协调在一个统一的框架体系。）

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。

本文通过我国股市的高频数据和相关性分析来研究市场群体的学习和心理行为。我们根据心理学中的操作性条件反射，首次提出一个交易性条件反射的概念，用成交量-价概率波方程中的成交量概率来计量市场群体交易性条件反射的强度。我们发现：总体来说，平均收益率与交易性条件反射强度变化之间具有显著的正相关性，市场群体对收益率的心理预期显著地表现了卖出的处置效应和买入的羊群行为，并且该“羊群”对价格趋势的心理预期明显地大于其反转的；第二，我们还发现在细分后的某一时期，它们之间具有显著的负相关性。我们用条件反射来解释他们的交易行为“异象”。

本文通过我国股市的高频数据和相关性分析来研究市场群体的学习和心理行为。我们根据心理学中的操作性条件反射，首次提出一个交易性条件反射的概念，用成交量-价概率波方程中的成交量概率来计量市场群体交易性条件反射的强度。我们发现：总体来说，平均收益率与交易性条件反射强度变化之间具有显著的正相关性，市场群体对收益率的心理预期显著地表现了卖出的处置效应和买入的羊群行为，并且该“羊群”对价格趋势的心理预期明显地大于其反转的；第二，我们还发现在细分后的某一时期，它们之间具有显著的负相关性。我们用条件反射来解释他们的交易行为。

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.