Portfolio and consumption decisions under ambiguity for regime switching mean returns

This paper examines a continuous-time intertemporal consumption and portfolio choice problem for an ambiguity-averse investor with multiple priors when the expected return of a risky asset is unobservable and follows a hidden Markov chain. The investor's beliefs over investment opportunities are represented by a set of priors over the process governing the dynamics of the conditional estimates of the unobservable state. The investor is assumed to have Chen and Epstein's (2002) recursive multiple priors utility preferences. Using the Malliavin calculus technique, we characterize the optimal consumption and portfolio rules explicitly in terms of the Malliavin derivatives and stochastic integrals. We find that continuous Bayesian revisions under incomplete information can generate an ambiguity-driven hedging demand that mitigates the intertemporal hedging demand for the risky asset. In addition, ambiguity aversion magnifies the importance of the intertemporal hedging demand.