Numerical methods for simulation of stochastic differential equations

Abstract

In this paper we are concerned with numerical methods to solve stochastic differential equations (SDEs), namely the Euler-Maruyama (EM) and Milstein methods. These methods are based on the truncated Ito-Taylor expansion. In our study we deal with a nonlinear SDE. We approximate to numerical solution using Monte Carlo simulation for each method. Also exact solution is obtained from Ito's formula. To show the effectiveness of the numerical methods, approximation solutions are compared with exact solution for different sample paths. And finally the results of numerical experiments are supported with graphs and error tables.