几类反射随机微分方程强解的数值仿真

反射随机微分方程在排队论、金融保险、存储系统建模、计算机网络研究中均具有广泛应用。文中回顾了反射随机微分方程的形式和方程解的定义,将无反射随机微分方程数值思想引用到反射情形,研究基于反射随机微分方程的Euler-Maruyama算法、Euler-Peano算法和惩罚数值算法。并以Ornstein-Uhlenbeck过程和反射Ornstein-Uhlenbeck过程为实例,对上述算法进行了仿真实验和比较。结果表明,在期权定价、利率期限结构、金融风险计算与受控金融市场建模等实际应用中具有良好的应用前景。

Numerical Simulations of Strong Solutions to Several Reflected Stochastic Differential Equation

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.