Optimal Solution of Investment Problems Via Linear Parabolic Equations Generated by Kalman Filter

We consider optimal investment problems for a diffusion market model with nonobservable random drifts that evolve as an Itôʹs process. Admissible strategies do not use direct observations of the market parameters, but rather use historical stock prices. For a nonlinear problem with a general performance criterion, the optimal portfolio strategy is expressed via the solution of a scalar minimization problem and a linear parabolic equation with coefficients generated by the Kalman filter.