Abstract: It is well-known that a financial model with deterministic coefficients are only good for a relative short period of time and cannot respond to changing conditions.The information available to the investor is the filtration generated by the asset price processes only.The investor can in general not directly observe the mean return rate processes and the volatility process of the asset price process.A simplified continuous time financial market with one risk-free asset(bond)and one risk asset(stock)were assumed.When the liability process is modeled by a linear-diffusion model and the mean return rates is modulated by a finite state continuous-time Markov chain,we estimate the mean return rates of stock under the Woham filter.By using the stochastic linear-quadratic control technique,the closed form solutions of the optimal portfolio strategy and the maximal expected exponential utility are obtained under the partial information.

Key words: Partial information, Liability, Linear diffusion model, Kalman filter , , Portfolio, Linear-quadratic control