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
DOI: 10.12677/SA.2017.62021, PDF, HTML, XML, 下载: 1,488  浏览: 3,792 
作者: 李乃明, 师恪*：新疆大学，数学与系统科学学院，新疆 乌鲁木齐
关键词: 前景理论；学习强度；敏感因子；The Prospect Theory； The Learning Strength； The Sensitive Factor
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。
Abstract: 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.
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. https://doi.org/10.12677/SA.2017.62021

参考文献

[1] Brock, W. and Hommes, C.H. (1997) A Rational Route to Randomness. Journal of Economic Dynamic Control, 65, 1059-1095.
https://doi.org/10.2307/2171879
[2] Brock, W. and Hommes, C.H. (1998) Heterogeneous Beliefs and Routes to Chaos in a Simple Asset Pricing Model. Journal of Economic Dynamic Control, 22, 1235-1274.
https://doi.org/10.1016/S0165-1889(98)00011-6
[3] He, X.Z. and Zheng, H.H. (2016) Trading Heterogeneity under Information Uncertainty. Journal of Economic Behavior Organization, 130, 66-80.
https://doi.org/10.1016/j.jebo.2016.07.001
[4] Bloomfield, R. and Hales, J. (2002) Predicting the Next Step of a Random Walk: Experimental Evidence of Regime-Switching Beliefs. Journal of Financial Economics, 65, 394-414.
https://doi.org/10.1016/S0304-405X(02)00147-2
[5] Chiarella, C., He, X.Z., et al. (2014) Heterogeneous Expectations in Asset Pricing: Empirical Evidence from the S&P500. Journal of Economic Behavior & Organization, 105, 1-16.
https://doi.org/10.1016/j.jebo.2014.03.003
[6] He, X.Z. and Li, Y.W. (2015) The Adaptiveness in Stock Markets: The Stylized Facts in the DAX30. Quantitative Finance Research Center, Research Paper 364.
[7] Lux, T. (1998) The Socio-Economic Dynamics of Speculative Market: Interacting Agents, Chaos and Details of Return Distributions. Journal of Economic Behavior & Organization, 33, 143-165.
https://doi.org/10.1016/S0167-2681(97)00088-7
[8] Naimzada, A. and Ricchiuti, G. (2013) Complexity with Heterogeneous Fundamentalists and a Multiplicative Price Mechanism. http://www.researchgate.net/publication/256089307
[9] De Grauwe, P. and Kaltwasser, P.R. (2007) Modelling Optimism and Pessimism in the Market. CESifo WP Series No, 1962, Foreign Exchange M.
[10] Park, B.J. (2002) On the Quantile Regression Based Tests for Asymmetries in Stock Return Volatility. Asian Economic Journal, 16, 175-191.
https://doi.org/10.1111/1467-8381.00147
[11] Nelson, D.B. (1991) Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica, 59, 347-370.
https://doi.org/10.2307/2938260
[12] Arkes, H.R., et al. (1988) The Role of Potential Loss in the Influence of Affect on Risk-Taking Behavior. Organizational Behavior and Human Decision Processes, 42, 191-193.
https://doi.org/10.1016/0749-5978(88)90011-8
[13] Kahneman, T. (1979) A Prospect Theory: An Analysis of Decision under Risk. Econometrica, 47, 263-291.
https://doi.org/10.2307/1914185
[14] Park, B.J. (2014) Heterogeneous Risk Aversion and Dynamics of Asset Prices among Boundedly Rational Agents. Journal of Banking & Finance, 43, 150-159.
https://doi.org/10.1016/j.jbankfin.2014.03.009
[15] Kukacka, J. (2016) Prospect Theory in the Heterogeneous Agents Model. Working Paper. http://www.researc-Chgate.net/publication/297574304
[16] 张晓萌. 含时变风险厌恶系数及其逆风参数的价格动态模型及实证分析[D]: [硕士学位论文]. 乌鲁木齐: 新疆大学, 2015.
[17] Hommes, C., Kiseleva, T., et al. (2012) Is More Memory in Evolutionary Selection (De) Stabilizing? Macroeconomic Dynamics, 16, 335-357.
https://doi.org/10.1017/S136510051000060X
[18] 王铎, 彭建平, 郑敏. 做市商调整价格速度与资产价格的波动[J]. 管理评论, 2004, 16(11): 28-34.
[19] 胡建梅. 含逆风参数的两类价格动态模型及实证分析[D]: [硕士学位论文]. 乌鲁木齐: 新疆大学, 2013.
[20] 张艳萍. 基于一类非线性价格预期函数的资产定价模型的研究[D]: [硕士学位论文]. 乌鲁木齐: 新疆大学, 2016.
[21] De Grauwe, P. and Grimaldi, M. (2003) Bubbling and Crashing Exchange Rates. CESIFO Working Paper Series, 1045.
[22] 周义仓, 曹慧, 肖燕妮. 差分方程及其应用[M]. 北京: 科学出版社, 2014.

为你推荐