Consumption and portfolio decisions with labor income and borrowing constraints

The authors develop a duality approach to study intertemporal consumption and portfolio decisions when an individual has limited opportunities to borrow against future labor income and cannot totally insure the risk of income fluctuations. An individual´s optimal consumption-portfolio problem is cast in continuous-time under both certainty and uncertainty frameworks. The duality approach makes it possible to characterize in a simple way the individual´s optimal consumption and portfolio policies when there are labor income and borrowing constraints. Sufficient conditions for the existence of a solution to the individual´s consumption and portfolio problem are established, and the optimal consumption and portfolio policies are analyzed via duality