Abstract: In this paper an asset price model described by hidden Markov process is considered, where is a standard Brownian motion and is an unknown constant. The mean return is a stochastic process not necessarily adapted to the filtration generated by the process and it contains some unknown parameters to be estimated from a continuous time observation of. Statistical estimators of the parameters and the parameters in based on Kalman filtering are proposed and some numerical simulations are performed for the proposed estimators.

Key Words: Hidden Markov process, Kalman Filter, parameter estimation, Stochastic Process.