含学习强度的资本资产定价模型分析精选.pdf

Statistics and Application 统计学与应用, 2017, 6(2), 178-190 Published Online June 2017 in Hans. /journal/sa /10.12677/sa.2017.62021 Research on Capital Asset Pricing Model with Learning the Strength * # Naiming Li , Ke Shi College of Mathematics and System Sciences, Xinjiang University, Urumqi Xinjiang rd rd th Received: Jun. 3 , 2017; accepted: Jun. 23 , 2017; published: Jun. 26 , 2017 Abstract Based on the prospect theory, the risk attitude of fundamentalists varies over time. If the devia- tion of the risk asset price from the fundamental price become more lager and lager, the risk aver- sion coefficient for fundamentalists will become smaller and smaller and then introduce a sensi- tive 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 bifurca- tion of model. Finally, we get the following conclusion: The learning strength has the effect of de- stroying the stability of the market and the sensitivity factor has the effect of stabilizing the market. Keywords 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 * # 李乃明 ，师 恪 新疆大学，数学与系统科学学院，新疆 乌鲁木齐 收稿日期：2017年6月3 日；录用日期：2017年6月23 日；发布日期：2017年6月26 日 摘 要 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 *第一作者。 #通讯作者。 文章引用: 李乃明, 师恪. 含学习强度的资本资产定价模型分析[J]. 统计学与应用, 2017, 6(2): 178-190. /10.12677/sa.2017.62021 李乃明，师恪 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。 关