Asset allocation and consumption smoothing under business cycle and state uncertainty

The paper investigates the optimal asset allocation and consumption problems under the assumption of mean-reverting stock return and unobservable state variable. The explicit solutions are given for the investors with power utility and habit formation, and the numerical solution is given for the investor with Epstein-Zin preference. Computation and simulations are conducted to examine the properties of the optimal strategies. We are especially interested in the consumption smoothing and find that the Epstein-Zin preference and habit formation will smooth the consumption stream while the classic investor will experience large changes of consumption.