分数阶扩散方程及数值解

Fractional Diffusion Equation and Its Numerical Solutions

该文对布莱克-斯库勒模型中的股票价格,运用莱维分布中判断时间非独立变量有非独立、稳定增值的充分必要条件处理求解缺陷,然后利用无风险利率对其进行简化,求得此股票价格的一个解,随之运用拉普拉斯变换及所得到的股票价格的解来研究欧体期权价值所满足的方程,试图得到欧体期权价值方程的数值解。

In this paper,introducing a sort of equation,we use Lévy process,risk-free rate to analyze this model,and then get a solution,then using Laplace transform and the solution which got from this model to express the equation which satisfies to the European-style,and try to analyze this diffusion equation with the property of fraction calculus and the fraction calculus called Grunwald-Letnikov to get the numerical solution.