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。)

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。

对恒生指数收益率进行自相关和条件异方差分析，剥离出平稳独立同分布的历史滤波噪音序列。假设噪音服从正态，及两类纯跳跃列维过程—调和稳态(CTS)、速降调和稳态(RDTS)，以建立风险中性条件Levy-GARCH模型进行期权定价。研究结果表明：噪音序列呈现尖峰有偏和肥尾的非高斯特征；调和稳态拟合与定价能力较正态好；资产价格存在跳跃速降趋势；布朗运动低估了金融市场震荡程度；速降调和稳态过程定价能力更加稳健。

：我们建立了一个包含居民、企业、银行部门的动态一般均衡模型。我们的模型 认为，实际利率的变动可以通过影响居民部门的储蓄和消费、企业部门的投资、银行部门的 吸存放贷，作用于就业和产出的变化。根据我们模型的分析，实际存款利率变动对产出的影 响取决于实际储蓄存款对实际存款净利率的弹性：富有弹性则稳态利率与产出同向变动、存 款利率有效上限的取消可能使产出总体上升；缺乏弹性则稳态利率与产出反向变动，存款利 率有效上限的取消可能使产出总体下降。 实际存款利率市场化导致的产出波动可能具有滞后 性和反向性。 稳态下实际贷款利率变动会改变资本相对劳动的价格、资本劳动之比和单位资 本产出。贷款利率有效下限的取消可能会使产出上升，实际贷款利率市场化影响产出的强度 可能与稳态贷款规模间接反向相关，但这种联系并不是必然的。

假设中外资银行分别具有信息优势和融资成本优势，本文构建了中外资银行多期动态竞 争的稳态模型，研究发现，中资银行仅靠“禀赋”的信息优势不足以抵挡外资银行进入的冲击， 多期竞争将使得外资银行更加容易进入中国市场，且更加可能成为竞争稳态的占优方。进一步 的比较静态结果显示：客户质量越好、项目收益越大和新市场增长越快，外资银行越可能稳态 占优；稳态占优方的市场份额随着项目收益和新市场增长速度的提高而减少，客户质量在中资 稳态占优和外资稳态占优两种情形下对占优方市场份额分别具有单调和非单调的影响。此外， 考虑中资银行相对熟悉市场的优势，我们对稳态模型进行了扩展分析。

世界各国政府积极地推行的通胀目标政策，导致了当前的流动性泛滥，价格的发散以及全球性通胀，利率的长期偏离又引致投机的盛行，低效的投资和资产泡沫的膨胀，当这种短期性增长不可持续时，经济将以危机收场，最终恢复至本来位置。本文在财政和货币政策协作机制下，建立了具有非零通胀稳态的粘性价格和粘性工资的新凯恩斯模型，研究了财政支配机制中的最优通货膨胀，分析表明：财政和货币政策共同决定通胀，财政支配机制中的最优通货膨胀正向偏离稳态，而这种偏离是以财政对因通胀产生的资源配置扭曲性影响的效用补偿为前提的，即当财政对社会存在效用的补偿时，才具有正向偏离稳态的最优通胀，这是“适度的通胀有益于经济增长”的唯一理由。同时，最优的实际利率大于零，且最优的名义利率为通胀与实际资本回报的比例之和，财政的补偿性效应的存在并不对利率和通胀政策产生实质性影响，即财政补偿效用和实际利率是对通胀所产生的资源配置的扭曲性影响的对价补偿。分析同时还表明财政和货币协作是治理通胀和平抑波动有效政策方式，通胀和利率相当于一个硬币的两面，两者长期的偏离不导致社会福利恶化的唯一可能性条件是财政对社会的效用补偿。

世界各国政府积极的通胀政策导致了当前的流动性泛滥，全球性通胀以及经济渐入下行通道，最终将导致深层次的经济调整以及社会福利的急剧恶化，而反映这一周期性经济现象的理论体系却也未能有效地解除危机的困扰。本文在财政和货币政策协作机制下，建立具有非零通胀的粘性价格和粘性工资结构特性的新凯恩斯模型，分析了Ramsey均衡下的最优通胀以及与之对应的最优利率。分析结果表明：确定性最优通胀为零，确定性最优利率应该等于通胀与因持有货币而放弃的无风险收益所获得的补偿之和；在Ramsey最优均衡下，最优通胀是一个相对于非零通胀稳态的紧缩率，并且紧缩的水平和程度在不同情形中呈现出较大的不一致性，同时，最优通胀要求最优实际利率大于零，并且最优的实际货币数量应该等于零，即名义货币数量不大于通胀水平。我们还对比分析利率规则与货币增长率规则之间的区别，结果表明财政政策会增加通胀趋势效应，货币增长率规则所引致的经济波动要比利率规则高，而高的波动性给经济造成了更多的不确定性，可能使通胀超出非零稳态的最优水平。在一个更加前瞻的视角上，这一组最优关系中利率作为持有货币而放弃的无风险收益的对价补偿，其长期的偏离最终可能会积聚资产泡沫为危机埋下隐患。