Dynamic Asset Allocation and Consumption Choice in Incomplete Markets

We study the optimal investment and consumption problem of a CRRA investor when the drift and volatility of the stock are driven by a correlated factor. The myopic and non-myopic components of the optimal portfolio process are characterized in terms of the market price of traded and non-traded risk of the minimax martingale measure. We find that the optimal policies depend crucially on the nature of the agent, aggressive versus conservative, and the market incompleteness, improving versus deteriorating investment opportunities. Furthermore, we show that the original problem cannot be decomposed into a pure consumption and a pure terminal wealth problem, unless the market is complete.