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This paper investigates the optimal selection of portfolios for power utilitymaximizing investors in a financial market where stock returns depend on ahidden Gaussian mean reverting drift process. Information on the drift isobtained from returns and expert opinions in the form of noisy signals aboutthe current state of the drift arriving randomly over time. The arrival datesare modeled as the jump times of a homogeneous Poisson process. Applying Kalmanfilter techniques we derive estimates of the hidden drift which are describedby the conditional mean and covariance of the drift given the observations. Theutility maximization problem is solved with dynamic programming methods. Wederive the associated dynamic programming equation and study regularizationarguments for a rigorous mathematical justification.

Portfolio Optimization in a Market with Hidden Gaussian Drift and Randomly Arriving Expert Opinions: Modeling and Theoretical Results