Abstract: The current real option pricing theory is based on the full information.In this paper,we relax this assumption and consider the optimal control problem of investment and consumption during an infinite horizon to explore the consumption-utility based indifference price of real option with partial observation,which is known as partial information.Thanks to Kalman filtering,dynamic programming and Hamilton-Jacobi-Bellman theory,an implied option value is given by the semi-closed-form solution to the two free-boundary PDE under the separation principle of control system and the numerical results are obtained by the finite difference method.Further more,by Monte Carlo simulation,the difference of strat egies between partial information and full information is discussed.Finally,we explore the relation of the two value functions under partial and full observation,and the economic value of information is derived.

Key words: real option, partial information, Kalman filtering, value of information