Numerical Approximation Methods for Solving Stochastic Differential Equations

Abstract

Stochastic differential equations (SDEs) models play a crucial role in many field of science such as biology, chemistry, climatology, mechanics, physics, economics and finance. In finance, the Black-Scholes stochastic differential equations are used to model the option price. The earliest work on SDEs was description on the Brownian motion done in Einstein’s paper “On the motion required by the molecular kinetic theory of heat of small particles suspended in a stationary liquid”. The Brownian motion plays an important role in SDEs. In this paper we will study some properties of SDEs and how to solve stochastic differential equation by applying the numerical approximation method.