| Differential equation has a certain application background. In the 70?s, the stochastic differential equations?diffusion process and stochastic analysis are widely employed in system engineering, engineering science, economics & finance and other fields. In recent years, the use of mathematical concept of random financial qualitative and quantitative analysis is becoming more and more common, especially in the quantitative research, such as the application of martingale and stochastic integral to get the option price and hedging strategy. With the changes of the integration and globalization of world economic are more and more intense, more economic subjects get more extensive trading in the wider economy market. At the same time, all sorts of phenomenon of financial and the economic market pattern deduce the uncertain and more complex changes under the influence of all kinds of uncertain dynamic factors. And the description of the phenomenon of complex financial is advancing by the stochastic differential equation theory. Such as Black-Scholes model to the classical Cox- Ingersoll- Ross model(CIR model) to the CIR model under regime switching, this model has a wide applicability. From the generalization promotion of the CIR model with regime switching, this article consider the interest rates mean reversion ? model with regime switching, which one is much more complex than CIR model with regime switching. To overcome the mathematical difficulties arising from regime switching as well as the non-Lipschitz coefficients, some special Lyapunov functions are developed. In this paper. We will investigate the global positive or nonnegative solution to the mean reversion ? model with regime switching, and then show that the EM solution converge to the exact solution, and estimation the parameter of model by maximum likelihood method and proof that the mean reversion ? model under regime switching is more applicable than mean reversion ? model. |
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