时滞均值回复θ过程及其数值解的收敛性

时滞均值回复θ过程用于描述受时间延迟影响的利率、波动率等金融特征,本文利用随机时滞微分方程理论证明了过程在1/2≤θ<1情况时解的存在唯一性和非负性.由于表示该过程的随机时滞微分方程没有显示解,所以数值近似解是研究过程的重要的方法,本文证明了时滞均值回复θ过程Euler-Maruyama数值解的p(p≥2)阶矩意义上的...

MEAN-REVERTING θ PROCESS WITH TIME DELAY AND THE CONVERGENCE OF ITS NUMERICAL SOLUTION

The mean-reverting θ process with delay is used as a model for interest rates and volatil-ity as well as other financial quantities which are past level dependent. For 1/2 ≤θ< 1, we prove the model has an unique nonnegative solution. Since the corresponding stochastic delay differential equation has no explicit solution, it is very important to study numerical meth-ods for the solution approximations. We prove the strong convergence of Euler-Maruyama approximate solution in sense of p-th moment(p≥2).