证券市场复杂行为分形标度分析与机会决策研究

【摘要】 以中国深市为研究对象,探讨BM在证券市场的适用性。研究表明中国证券市场存在相关性,表现为分形时间序列,其行为不符合BM运动性质,而服从分数布朗运动(FBM)。标度分析表明市场存在短周期和长周期,并给出了周期值。在行为心理学框架下对时变Hurst指数演变形式进行了分析,分析了在市场不同阶段,时变Hurst指数揭示的市场易变行为、均值回复、长程相关性。证明了分数布朗运动的Ito微分方程-F-Ito微分方程,在此基础上给出了分数布朗运动下的Black-Scholes公式(F-Black-Scholes公式),使Black-Scholes公式成为其特例。讨论了H指数对投资决策的影响,给出此时根据H指数的投资决策的步骤和策略。更多还原

【Abstract】 As a sample, Shenzhen Stock Market is researched depending on R/S analysis .It indicates correlation exists in Shanghai stock market, and the behavior represents fractal time series and subjects to fractal time series (FBM). The scale analysis makes clear that it indicates there are a long period and a short period in the market. In the frame of behavior psychology, analyze variability mean reverting, long run correlation basing on vary-time H index on different stage. The Ito-Differential Equation of FBM is given, and further more Black-Scholes formula of FBM(F-Black-Scholes formula) is given. The influence of H index on investment decision making is discussed. Finally, steps and tactics to make investment decision are given out on the basis of H index.更多还原