Abstract: In this paper an asset price model described by hidden Markov process dS(t) = μ(t)S(t)dt + σS(t)dW(t ) is considered, where W is a standard Brownian motion and σ is an unknown constant. The mean return{μ(t), 0 ≤ t ≤ T} is a stochastic process not necessarily adapted to the filtration generated by the process {S(t), 0 ≤ t ≤ T} and it contains some unknown parameters to be estimated from a continuous time observation of S(t). Statistical estimators of the parameters σ and the parameters in μ 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.