Asset Allocation under Imperfect Information: Closed-Form Consumption and Portfolio Choice under Incomplete Markets

This paper studies consumption and portfolio choice under incomplete markets and parameter uncertainty. I establish the necessary conditions under which the investor’s optimization problem under incomplete markets can be transformed into a complete markets problem. This paper extends the literature on asset allocation by obtaining closed form solutions to the consumption and portfolio problem of an investor with incomplete information about variables which determine the changes in the investment opportunity set and by stating a set of conditions which allow the treatment of the incomplete markets consumption and portfolio choice problem with martingale methods developed in the complete markets framework. The methodology presented in this paper bridges the gap between the numerical and approximate solutions found in incomplete markets consumption and portfolio choice problems and the closed-form solutions found in complete markets consumption and portfolio choice problems.