Existence Theorem for Mean-Reverting CEV Process with Regime Switching

Empirical studies show that the most successful continuous-time models of the short term rate in capturing the dynamics are those that allow the volatility of interest changes to be highly sensitive to the level of the rate. The mean-reverting constant elasticity of variance (CEV) process with regime switching is a stochastic differential equation that has found considerable use as a model for interest rate, volatility, and other financial quantities. Since the coefficients of CEV process do not satisfy the linear growth condition, we can not examine its properties by traditional techniques. This paper overcomes the mathematical difficulties due to the nonlinear growth of the meanreverting CEV process with regime switching, and provides a detailed proof that there is a unique positive global solution for such SDE.