研究了马尔科夫切换型资产定价模型的随机theta方法的渐近稳定性和$P$阶矩指数稳定性,给出了$p$阶矩指数不稳定的一个充分条件,证明了非线性随机微分方程随机theta方法的渐近稳定性.

In the paper, we study the asymptotically stability and the exponential stability of the pth moment for asset price model with Markovian switching. More-
over, we give a sufficient condition for the exponential instability of the  pth moment.Finally, we show the exponential stability of stochastic theta method for nonlinear hybrid stochastic differential equation.