Consumption-portfolio optimization and filtering in a hidden Markov-modulated asset price model

We study a consumption-portfolio optimization problem in a hidden Markov-modulated asset price model with multiple risky assets, where model uncertainty is present. Under this modeling framework, the appreciation rates of risky shares are modulated by a continuous-time, finite-state hidden Markov chain whose states represent different modes of the model. We consider the situation where an economic agent only has access to information about the price processes of risky shares and aims to maximize the expected, discounted utility from intermediate consumption and terminal wealth within a finite horizon. The standard innovations approach in filtering theory is then used to transform the partially observed consumption-portfolio optimization problem to the one with complete observations. Robust filters of the chain and estimates of some other parameters are presented. Using the stochastic maximum principle, we derive a closed-form solution of an optimal consumption portfolio strategy in the case of a power utility.