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 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 crowd’s trading behavioral hypotheses relevant to the volume uncertainty associated with price in China stock market. The empirical work reveals that market crowd trade in simple heuristics and efficient adaptation, 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 among themselves no matter whether it is highly overestimated or underestimated, suggesting that asset prices include not only a fundamental value but also private information, speculative, sentiment, gamble, and entertainment values etc. In addition, 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交易量与价格之间不确定关系中关于群体交易行为的两个基本假说。实证结果表明：市场群体在每日交易的时间窗口内采用简单的经验法则和有效的适应方式来从事交易，并且总是逐步地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基本价值同时还包含非公开信息、投机、情绪、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。)

本文在理性预期的框架下构建模型，通过定价偏差、信息揭示程度、市场深度和价格波动 分析了连续交易机制和停牌制度之间的差异。研究结果表明，连续交易和停牌的优劣，实际上取决于市场 知情者人数的多少；而公告信息精度的高低，也在另一方面决定了停牌实施的效果。另外，本文使用中国 股票市场的停牌和交易数据对理论模型进行了相关检验。结果发现，在中国股票市场，无论是例行停牌还 是警示性停牌，停牌后的市场深度和价格波动总是大于非停牌日平均水平，这表明中国股市的停牌在一定 程度上并没有达到优于连续交易的预期效果。

信息操纵与内幕交易是市场经济的敌人，而惯性交易策略是市场经济的忠诚护卫者，她将有利于扫荡市场经济中的无耻恶行。 “基于自适应控制数理建模的股票（期货）投资系统”采纳广泛而有意义的数理原理，即连续博弈过程中所必须的工具，而不是预先确定一个（非回归）精炼方程，以企图描述复杂系统的演化进程。本系统将鞅论、小波分析、神经网络算法、非线性动力学、湍流不动点、自适应鲁棒控制、进化争当少数获胜博弈、行为金融学、及复杂科学系统等数学物理理论融于一体；对开放的、自组织的连续交易分形市场，拟合非线性随机差分方程，随机逼近波动函数极值dx/dt=0，以辨识无特征尺度波动转捩点，并建立相应匹配资金管理系统模型，从而实行基于不动点的反向与惯性行为金融交易；并通过分析离散时间、价格区间股票（期货）买卖交易量及残差量序列变化，建立惯性的动态系统交易技术模型；依据市场供求关系（相对增量资金买入推动上涨趋势，相对增量头寸抛压促发下跌趋势），跟踪价格波动方向，将非线性混沌市场交易化归为多尺度拟线性递推形式，从而获取具多物理量，能有效监测价格波动惯性、跟踪市场趋势，提供交易决策的量化标准，可帮助实现市场压力测试及套利操作。 “基于自适应控制数理建模的股票（期货）投资系统”由马金龙和马非特独立创建，具有自主知识产权。其特点是有气象预报一样的数值分析；有地震预测一样的物理原理；有弹道导弹一样的航位推算；独创股票（期货）惯性交易策略。