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We consider optimal investment problems for a diffusion market model withnon-observable random drifts that evolve as an Ito's process. Admissiblestrategies do not use direct observations of the market parameters, but ratheruse historical stock prices. For a non-linear problem with a generalperformance criterion, the optimal portfolio strategy is expressed via thesolution of a scalar minimization problem and a linear parabolic equation withcoefficients generated by the Kalman filter.

Optimal solution of investment problems via linear parabolic equations generated by Kalman filter