根据前景理论,对于基本面分析者引入时变的风险厌恶系数,假定当风险资产的价格偏离其基本价值越大时,基本面分析者的风险厌恶系数将越小,进而引入一个敏感因子。对于图表分析者我们引入一个含学习强度的非线性价格预期函数。运用差分方程的理论分析了确定性模型的平衡解、稳定性及其分支情况,通过对确定性模型的分析我们得出学习强度具有破坏系统稳定性的作用而敏感因子具有稳定系统的作用。
Based on the prospect theory, the risk attitude of fundamentalists varies over time. If the deviation of the risk asset price from the fundamental price become more lager and lager, the risk aversion coefficient for fundamentalists will become smaller and smaller and then introduce a sensitive factor. To the chartists by considering a nonlinear function impacted by the learning strength. Using the theory of difference equation, we analyze the equilibrium solution, stability and bifurcation of model. Finally, we get the following conclusion: The learning strength has the effect of destroying the stability of the market and the sensitivity factor has the effect of stabilizing the market.
前景理论,学习强度,敏感因子, The Prospect Theory The Learning Strength The Sensitive Factor含学习强度的资本资产定价模型分析
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1. 引言
与传统的金融模型相比,现如今的金融模型往往考虑含不同信念的交易者:即异质信念模型。如:Brock and Hommes [1] [2] 考虑了两类交易者:基本面交易者和图表分析者。其中基本面交易者认为资产价格长期将返回到其基本价值而图表分析者期望过去的价格趋势能持续下去。基本面分析者往往被认为是理性交易者,具有稳定市场的角色;图表分析者则往往被认为是非理性交易者,具有破坏市场稳定的角色。在文献 [3] 中Xue-Zhong He指出当风险资产的价格偏离其基本价值越来越大时,市场中的基本面分析者将会变的越来越多,从而使风险资产的价格返回到基本价值,表现出稳定市场的角色;当风险资产的价格越来越接近其基本价值时,市场中的图表分析者将会变的越来越多,从而使风险资产的价格偏离其基本价值,表现出破坏市场稳定的角色。这种异质交易者的相互转化,正是异质模型的一大特点,Bloomfield and Hales [4] 为此提供了实验证据。基于此,不同的学者建立了不同的转换交易策略。主要分为:同步转换交易策略和不同步转换交易策略。Chiarella and He [5] 用同步转换交易策略证实了市场中基本面交易者和图表分析者的存在性,市场开始时是由基本面分析者占据主导地位,但随着时间的推移,图标分析者将占据主导地位,这两类交易者是可以相互转化的。Xue-Zhong He and You-Wei Li [6] 建立了不同步转换交易策略。
参照Degrauwe and Grimaldi [21] ,假定当价格偏离其基本价值越大时,其风险系数将会变小,当价格偏离基本价值太大时,此时的敏感度将会变大,基本面分析者将会增加其市场份额。从我们定义的(7)式和(8)式来看,我们可得到类似的结论,当敏感度变大或者价格偏离基本价值变大时,风险系数将会变小,从而基本面分析者将会增加市场分额,进而稳定市场。
李乃明,师恪. 含学习强度的资本资产定价模型分析Research on Capital Asset Pricing Model with Learning the Strength[J]. 统计学与应用, 2017, 06(02): 178-190. http://dx.doi.org/10.12677/SA.2017.62021
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