A Two-parameter Simulation Of Price Movements Fractal

Price movements in financial markets there are complexity and variability owing to interactions of multiple factors, there are also scale invariance.we should apply fractal theory to better characterize the expression of market price movements and thus accu-rate interpretation of the information contained in the market price movements.Even if the volatility of financial markets,fractal theory are of great significance. As an attempt and exploration, this paper constructs a simulated price movements Two-parameter fractal,and probe the fractal dimension,box dimension and Hausdorff dimension of the fractal. And we study some of the structural characteristics of the fractal,and discuss the relevance between fractal parameters and the market price fluctuations.The paper is divided into three chapters.In chapter one, we constructed a fractal with two parameters using Mandelbrot's method,and give the iterated function system of the fractal.In chapter two,we calculate the fractal's fractal dimension,box dimension and Hausdorff dimension,and they are the same to dimH where (0<μ<γ<1).In chapter three,we discuss the fractal's continuity and smooth-ness based on parameters ofγ,μ,and make a brief analysis about the influence on the fractal's dimension and the correlation between of market price fluctuations based on two parameters.This paper mainly results:Theorem 1.2.4 Iterated function systems IFS of two-parameter fractal is {E; W1,W2,W3},and F(?)E meet where Theorem 2.2.1 The box dimension,fractal dimension and Hausdorff dimension of two-parameter fractal are the same to where(0<μ<γ<1),Theorem 3.1.3 Two-parameter fractal F is the attractor of the IFS{E,Wn,n= 1,2,3}.When 0<μ<γ<1, VB∈H(E),then F(λ)is continuous about,γ,μin the Hausdorff metric.whereTheorem 3.2.1 f is the function of two-parameter fractal,then where and C=max{2γ,4(1+μ-γ)},0<μ<γ<1.