基于Parareal算法的CIR模型数值保正性研究

Research on the Numerical Positivity-Preserving of the CIR Model Based on the Parareal Algorithm

CIR(Cox-Ingersoll-Ross)模型本身对数值算法具有保正性要求。因此,本文进行了隐式Euler方法作为粗细因子、Milstein方法作为粗细因子等4种不同组合的Parareal算法对CIR模型的数值计算,数值研究了Parareal算法在不同扰动值下的保正性及均方误差收敛性。结果表明,上述考虑的Parareal算法具有均方收敛性和数值保正性。

CIR(Cox-Ingersoll-Ross)model itself has the requirement of preserving the correctness of the numerical algorithm.Therefore,in this paper,Parareal algorithm with four different combinations of implicit Euler method as the thickness factor and Milstain method as the thickness factor is performed for the numerical calculation of CIR model,and the positivity-preserving properties and the convergence of the mean square error of Parareal algorithm under different disturbance values are numerically studied.The results show that the Parareal algorithm has mean square convergence and numerical positivity.