噪音条件下的资产价格行为分析与投资组合管理研究

The existence of noise in the market makes the transaction price can't reflect the fundamental value of asset precisely, which raised a big challenge to the efficient market hypothesis (EMH). On the basis of hypothesis that asset price obey Wiener process for traditional finance, our study builds the asset price equation containing noise, then uses state space model and Kalman filter methods to estimate the trajectory of the noise, which by introducing noise path to change rate of return characteristics of the price equation, also relaxing the conditions of non-noise rate of return and time-varying volatility, price and volatility jump phenomenon of Wiener process. Also tests the effectiveness and robustness of the estimation method by the methods of simulation tools and artificial market simulation. Simultaneously, we study the problem of asset pricing considering the noise, investigate how noise affects the asset price behavior and explains the market anomaly phenomenon. Further, the research attempts to systematically study the distribution pattern characteristics of noise level and it's fluctuations in the dynamic structure by adopting mathematical derivation and simulation methods, and analyzes the effect of noise on distribution of rate of return of assets. Finally, based on the theory of mean-variance, the topic researches how noise affects the income of covariance matrix and effective border on portfolio, and builds risk metrics containing noise components to examine the problem of portfolio.

市场噪音导致交易价格不能确切地反映资产基础价值，对有效市场假说提出了极大的挑战。本课题拟在资产价格服从布朗运动的基础上，通过引入噪音路径改变价格方程的收益率项特征，并从非噪音收益率和波动率项时变及价格和波动的跳跃现象角度对布朗运动进行放松，构建包含噪音的资产价格方程，进而利用状态空间模型和卡尔曼滤波等方法估计噪音的运动轨迹，并通过仿真手段和人工市场模拟来检验估计方法的效果和鲁棒性。同时实证研究考虑噪音的定价问题，探讨噪音如何影响资产价格行为及解释市场异象。进一步采用数理推导和仿真模拟的方法系统性地探究噪音水平的分布形态特征及其波动的动态结构，并分析其对资产整体收益率分布形态的影响情况。最后通过仿真和实证方法基于均值-方差理论探寻噪音对投资组合的收益协方差阵和有效边界的影响，并通过构建含有噪音成分的风险度量指标深入研究投资组合问题。

市场噪音导致交易价格不能确切地反映资产基础价值，对有效市场假说提出了极大的挑战。本课题在资产价格服从布朗运动的基础上，通过引入噪音路径改变价格方程的收益率项特征，并从非噪音收益率、波动项时变以及价格的波动跳跃现象角度对布朗运动进行放松，构建包含噪音的资产价格方程，进而利用相空间方法和卡尔曼滤波等方法估计包含噪音的价格过程，并通过仿真手段来检验估计方法的效果和稳健性。其次，采用数理推导和仿真模拟的方法系统性地探究噪音水平的分布形态特征及其波动的动态结构，分析其对资产整体收益率分布形态的影响情况。同时，从理论层面构建包含噪音的交易过程并对其进行刻画，进一步探讨噪音如何影响资产价格行为与定价过程。再次，基于大数据技术从实证角度剖析了噪音条件下的投资者交易行为与信息传递过程。最后，在Markowitz均值-方差框架下构建了包含噪音的投资组合选择理论，使该理论更加符合实际投资环境。