私有内部信息条件下的两阶段做市定价规则研究

In traditional market microstructure models, informed traders have inside information on the assets value and market makers understand the quality of the inside information (the distribution of the value of assets). While it is convenient to assume that the prior of inside information is common knowledge, it may well be that market makers know little about the quality of inside information. In this research program, we propose models where the informed trader receives a signal correlated with the true asset value and knows how closely the correlation is, while the market makers know neither the signal nor the correlation but the distributions of them respectively. Hence, we modify the traditional framework by introducing another layer of uncertainty - the quality of the private signal. The informed trader has private inside information. Correspondingly, we model the market making process as two-stage lotteries (lotteries having as outcomes for other simple lotteries)and apply the rank-dependent expected utility theory on two-stage lotteries to solve the market making process. The informed trader makes more profit with 'two-stage market making' where the market makers employ a certainty-equivalent mechanism than with the more intuitively appealing 'reduction market making' where the market makers simply multiply the probabilities of the two stages, and the market price reflects more private information of the informed at the same time..We then apply dynamic consistency in the non-expected utility theory literature to extend analysis of two-stage market making to a dynamic trading model with long-lived private inside information. The informed trader trade rounds and market makers set the prices following two-stage market making at each round. The information structure in the first round is the same as in the static one. Since both the informed trader and market makers need to make inferences from the previous trading rounds, the information environment evolves over time. The dynamic model enables us to study the dynamic trading strategy of the informed and explore the dynamic patterns of price efficiency and market liquidity..An alternative modeling of the market making process is to interpret the unknown correlation as ambiguity faced by market makers and to study market making models by using the subjective expected utility (SEU) theories under ambiguity. We adopt five widely used models of ambiguity-averse preferences, namely Choquet expected utility, maxmin expected utility, variational preferences, Alpha-maxmin, and the smooth model of ambiguity aversion to analyze both static and dynamic market making models and apply dynamic consistency to ensure a recursive relation for the dynamic models. Moreover, SEU theories under ambiguity are employed to study other problems in market microstructure such as the information-based models, strategic trader models, the price process, market liquidity, market segmentation, and different trading mechanism.

本项目放松传统市场微观结构模型中内部人与做市商掌握资产价值信息的假设，引入与资产价值相关信号的概念，假设内部人收到该信号，并确切知道其与资产价值的相关性，而做市商仅知道相关性的概率分布。此时做市商面临的不确定是一个典型的两阶段彩票，称其行为为两阶段的做市过程。运用两阶段彩票顺序依赖期望效用理论[RDEU]研究内部人的策略交易决策、市场流动性和价格有效性；进一步运用RDEU动态相容性把此内部私有信息问题扩展到离散动态模型（内部人利用私有信息进行多期交易，且每次交易做市商都遵循两阶段做市规则），研究内部人动态交易策略、市场有效性和流动性的动态变化过程；最后，引入暧昧主观期望效用理论及其递归推广，研究用暧昧表示的两阶段彩票私有内部信息及相关的其他问题，如信息模型、价格过程、市场分割、交易规则等。

本项目重点研究两层信息结构、私有内部信息、暧昧信息框架等基础上的金融经济学问题，包括资产定价、不完全投资组合、限制交易之谜等。不同交易者对公司或者股票价值的概率分布有一定认知，但是对其相依关系认知需要不同的背景，经济人的决策融入风险与暧昧，天真(Naive)交易者的需求函数是逐段线性连续但不光滑，并且可能绝对值大于熟练(Sophisticated)交易者的需求函数，为了避免相关系数暧昧环境天真交易者的理性决策导致限制交易。在均衡状态，较低质量的资产产生较高的超额收益。均衡的比较静态分析说明天真交易者的比例与暧昧水平可以改变均衡类型，但是对资产价格的影响不是单调的。这项研究解决了限制交易之谜，并且说明谜底来自不同交易者对资产之间相关系数的认知差异，掌握信息较少的天真(Naive)交易者有可能不愿意参与交易。金融科学中这个重要的理论改变人们对不完全投资组合的理解，Journal of Financial Markets (SSCI检索金融科学顶级期刊之一)主编Gideon Saar(Cornell大学金融学教授)很愉快地接收发表这个诱人的结果。在光滑暧昧模型框架下我们假定透明交易者对额外投资机会回报率的标准差(方差, 投资风险)存在暧昧, 这种认知暧昧性抑制了透明交易者的投资行为, 会导致风险资产溢价过高及社会福利损失。透明交易者是暧昧厌恶的投资者, 其投资决策依据光滑暧昧厌恶模型, 需求函数呈现连续且光滑的特征。而隐蔽交易者通过支付一定的信息获取成本获得私有信息具有信息优势, 他们是标准的风险厌恶的投资者。通过构建理性预期均衡, 我们的研究发现: 初始资产严格为正的透明交易者将获得严格为正的超额收益; 提高信息获取成本将减少隐蔽交易者的比例, 从而增加风险资产溢价, 降低福利水平, 因而不是一项好的管制措施; 而旨在提高市场透明度降低交易者暧昧性的举措总有利于提高福利水平。

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