一类非线性的金融模型及其EM数值解

A Nonlinear Finance Model and Its Euler-Maruyama Numerical Solution

证明了一类高度非线性的随机微分方程形式的金融模型的解析性质,包括非负全局解的存在唯一性、EM解的收敛性。另外,还说明了基于EM算法的蒙特卡洛模拟可计算各类金融产品的预期收益率。

The analytical properties about a highly nonlinear stochastic differential equation model in finance were dis- cussed,which mainly included the unique global positive solution and the convergence of Euler - Maruyama approximate solutions. Moreover, the convergence result justified clearly that the Monte Carlo simulations based on the EM method could be used to calculate the expected payoff of financial products.