利用模糊意见网络建模股价动态
Modeling Stock Price Dynamics with Fuzzy Opinion Networks
AI总结：
本文提出通过社交网络建模投资者之间的口碑交流，探讨投资者社交网络变化对股价动态的影响。采用高斯模糊集建模投资者，通过邻居的输出平均值确定中心，利用不同参考方案建模不确定性，证明在局部参考方案下投资者会分组，而在全局或外部参考方案下会达成共识。
摘要：
我们提出一个数学模型，用于通过社交网络建模股票投资者之间的口碑交流，并探讨投资者社交网络的变化如何影响股价动态，反之亦然。一个投资者被建模为一个高斯模糊集（一个模糊意见），其中心和标准差作为输入，模糊集本身作为输出。投资者连接方式如下：一个投资者的中心输入取其邻居的输出平均值，其中如果两个投资者的模糊意见足够接近则被视为邻居，标准差（不确定性）输入则采用局部、全局或外部参考方案来建模不同情况下投资者如何定义不确定性。模糊意见的中心和标准差分别代表预期价格及其不确定性，作为价格动态方程的输入。我们证明，使用局部参考方案时，投资者在有限时间内收敛到不同的群体，而使用全局或外部参考方案时，所有投资者在有限时间内收敛到共识，且在外部参考情况下的共识可能随时间变化。我们展示了如何在该数学框架内建模趋势追随者、反趋势者和操纵者，并证明操纵者的最大敌人是其他操纵者。我们通过蒙特卡洛模拟展示了模型参数如何影响价格动态，并将修改后的模型应用于2013年12月5日至2015年12月4日期间香港十五家顶级银行和房地产股票的每日收盘价，发现综合不确定性急剧增加是预测当前价格趋势反转的可靠信号。
英文摘要：
We propose a mathematical model for the word-of-mouth communications among stock investors through social networks and explore how the changes of the investors' social networks influence the stock price dynamics and vice versa. An investor is modeled as a Gaussian fuzzy set (a fuzzy opinion) with the center and standard deviation as inputs and the fuzzy set itself as output. Investors are connected in the following fashion: the center input of an investor is taken as the average of the neighbors' outputs, where two investors are neighbors if their fuzzy opinions are close enough to each other, and the standard deviation (uncertainty) input is taken with local, global or external reference schemes to model different scenarios of how investors define uncertainties. The centers and standard deviations of the fuzzy opinions are the expected prices and their uncertainties, respectively, that are used as inputs to the price dynamic equation. We prove that with the local reference scheme the investors converge to different groups in finite time, while with the global or external reference schemes all investors converge to a consensus within finite time and the consensus may change with time in the external reference case. We show how to model trend followers, contrarians and manipulators within this mathematical framework and prove that the biggest enemy of a manipulator is the other manipulators. We perform Monte Carlo simulations to show how the model parameters influence the price dynamics, and we apply a modified version of the model to the daily closing prices of fifteen top banking and real estate stocks in Hong Kong for the recent two years from Dec. 5, 2013 to Dec. 4, 2015 and discover that a sharp increase of the combined uncertainty is a reliable signal to predict the reversal of the current price trend.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
