本文研究股票市场中的交易量权重价格动态均衡，用最大交易量权重价格表示价格参照点或均衡点。我们假设日内股价由于动量效应不断地偏离该价格均衡点，又由于反转效应重新返回，并且交易量权重在价格区间的分布服从一组解析的交易量权重价格动态均衡模型。通过量化动量交易、反转交易和相互作用交易，我们构建了价量概率波二阶微分方程，得到了交易量权重价格动态均衡的数学模型，并且用相互一致性偏好来解释该动态均衡的形成机制。利用我国 A 股市场每笔交易的高频数据进行实证检验，表明了该模型的有效性。交易量权重价格动态均衡模型的数学表达式包含了期望效用理论、前景理论和反射理论的主要内容，具有很好的应用前景，例如可以建立相互作用条件下的动态均衡风险模型及其风险管理。

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。)

不确定性决策的研究具有重大的理论和实践意义。阿莱悖论和行为金融的实验结果是不确定性决策中“非期望效用理论”发展的基础。为了检验阿莱悖论和行为金融权重函数的性质，本文在广泛的群体组织了经济实验，结果表明阿莱悖论和行为金融学中决策权重函数的性质在并不是普遍成立的。本文的实验结果与其他学者在海外华人相关实验结果相印证，对以阿莱悖论和行为金融权重函数为基础的理论体系构成了根本性的质疑，为新的不确定性决策理论发展提供了实验依据。

指数贴现效用理论与预期效用理论分别研究时间维度和风险维度下的偏好选择，是新古典标准范式的两大支柱偏好选择理论。然而，近年来的研究发现，市场上存在着许多用这两种效用理论难以解释的“异常”。目前，行为金融学中的前景理论（prospect theory）对预期效用理论的替代已逐渐为人们接受，国内介绍也比较细致；而在同样取得重大突破的时间偏好领域，其研究分析框架的转换则还没有引起足够的重视。本文拟从范式转换的角度，对时间偏好理论的发展作一全面回顾，着重介绍80年代以来行为经济学在该领域的突破??双曲线贴现模型，希望以此推动国内这方面的研究。