关键词: Euler Maruyama算法, Euler Peano算法, 惩罚数值算法

Abstract:

Reflected stochastic differential equations are widely applicable in queuing theory,banking and insurance,storage system modeling,and computer network.In this paper,we first review the form and the definition of the solution to reflected stochastic differential equation.Then we apply the numerical idea of non-reflected stochastic differential equation to reflected cases.The Euler-Maruyama algorithm,the Euler-Peano algorithm and the penalization algorithm are proposed to study the numerical solutions to the reflected stochastic differential equation.Finally,taking the Ornstein-Uhlenbeck process and reflected Ornstein-Uhlenbeck process as examples,we perform simulations and compare the results of the above algorithms.The results show that the proposed algorithms have good prospects in the practical applications of option pricing,term structure of interest rates,financial risk calculation and the modeling of controlled financial markets.

Key words: Euler Maruyama algorithm;Euler Peano algorithm;penalization algorithm