Portfolio optimization under partial information with expert opinions
We investigates optimal portfolio strategies for utility maximizing investors in a market with partial information on the drift. The drift is modelled by a continuous-time Markov chain with finitely many states which is not directly observable. Information on the drift is obtained from the observation of stock prices. Moreover, and this is the novel feature of this paper, expert opinions are included in the analysis. This additional information is modeled by a marked point process with jump-size distribution depending on the current state of the hidden Markov chain. We derive the filtering equation for the return process and incorporate the filter into the state variables of the
optimization problem. For this reformulated completely observable problem we investigate for the case of power utility the associated Hamilton-Jacobi-Bellman equation. Since this equation contains non-linearities in a jump part we adopt a policy improvement method to obtain an approximation of the optimal strategy. Numerical results are presented.