Stochastic growth: a duality approach

We re-examine the representative agent's optimal consumption and savings under uncertainty in the presence of investment constraints using martingale representation and convex analysis techniques. This framework allows us to explicitly quantify precautionary savings which induces a higher average growth rate than in a certainty setup. We provide a closed form solution for a Cobb-Douglas economy. The effect of uncertainty on portfolio selection is analyzed. Consumption growth rate and risk free interest rate exhibit a U-shaped relationship. Uncertainty negatively affects expected consumption growth rate; such a result seems to be supported by empirical evidence.