Before revision: This paper studies the parabolic free boundary problem arising from pricing American-style put options on an asset whose index follows a time-homogeneous diffusion process. The time-homogeneous diffusion process in this paper includes the geometric Brownian motion process , the CEV process, the mean-reverting Gaussian process or the Vasicek model, and the mean-reverting square root process or the CIR model.
After revision: This paper studies the parabolic free boundary problem arising from pricing American-style put options on an asset whose index follows a geometric Brownian motion process , the CEV process, the mean-reverting Gaussian process or the Vasicek model, and the mean-reverting square root process or the CIR model.