Labor income, borrowing constraints, and equilibrium asset prices

Abstract

We develop a duality approach to study an individual's optimal consumption and portfolio policy when the individual has limited opportunities to borrow against future labor income and cannot totally insure the risk of income fluctuations. The individual's intertemporal consumption and portfolio problem is cast in a continuous-time setting under uncertainty. We transform the individual's intertemporal problem into a dual shadow prices problem that solves the shadow prices for the individual's optimal consumption plan or equivalently the individual's intertemporal marginal rates of substitution. We show that the shadow prices process can be expressed as a product of a martingale and a decreasing process (normalized by the bond price). The existence of an optimal solution to the individual's intertemporal consumption and portfolio problem is established via duality. The duality approach also allows us to characterize in a sample way the individual's optimal consumption and portfolio policy in the presence of labor income and borrowing constraints. Equilibrium implications of borrowing constraints on asset prices are also discussed in the paper.