Stochastic growth: a duality approach. (Q1420881)

This paper investigates 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 explicity quantify precautionary savings which induced a higher average growth rate than in a certainty setup. The effect of uncertainty of the portfolio selection is analyzed. Consumption growth rate and risk free interest rate exhibit a \(U\)-shaped relationship.