Black-Sholes方程的解析解及收敛性分析

Analytical solution and convergence analysis of Black-Sholes equation

将经典的Black-Sholes方程转化为一类特殊的线性偏微分方程,并通过对其采用Fourier变换方法求得解析解,最后利用优核的相关性质对所得Black-Sholes方程解析解进行收敛性分析,证明了该解析解的收敛性.

In this paper,the classical Black-Sholes equation is translated into a special class of linear partial differential equations whose analytic solutions can be found by using Fourier transform method.Furthermore,the convergence of the analytical solution is discussed by using the properties of good kernel.The analytical solution is proved to be convergent.