Portfolio optimization for a large investor under partial information and price impact

This paper studies portfolio optimization problems in a market with partial information and price impact. We consider a large investor with an objective of expected utility maximization from terminal wealth. The drift of the underlying price process is modeled as a diffusion affected by a continuous-time Markov chain and the actions of the large investor. Using the stochastic filtering theory, we reduce the optimal control problem under partial information to the one with complete observation. For logarithmic and power utility cases we solve the utility maximization problem explicitly and we obtain optimal investment strategies in the feedback form. We compare the value functions to those for the case without price impact in Bauerle and Rieder (IEEE Trans Autom Control 49(3):442-447, 2004) and Bauerle and Rieder (J Appl Prob 362-378, 2005). It turns out that the investor would be better off due to the presence of a price impact both in complete-information and partial-information settings. Moreover, the presence of the price impact results in a shift, which depends on the distance to final time and on the state of the filter, on the optimal control strategy.