Portfolio optimization for a large investor controlling market sentiment under partial information

We consider an investor faced with the utility maximization problem in which the risky asset price process has pure-jump dynamics depending on an unobservable Markov chain, with intensity controlled by actions of the... [ view full abstract ]

We consider an investor faced with the utility maximization problem in which the risky asset price process has pure-jump dynamics depending on an unobservable Markov chain, with intensity controlled by actions of the investor. Using filtering, we reduce this problem with partial information to one with full information. We apply control theory for piecewise deterministic Markov processes to solve the  problem. We provide a toy example with a two-state Markov chain, and discuss how investor's ability to control the intensity of the state process affects the optimal portfolio strategies under both partial and full information.