Optimal consumption and equilibrium prices with portfolio constraints and stochastic income

This paper examines the intertemporal optimal consumption and investment problem in the presence of a stochastic endowment and constraints on the portfolio choices. Short-sale and borrowing constraints, as well as incomplete markets, can be modeled as special cases of the class of constraints we consider. Existence of optimal policies is established under fairly general assumptions on the security price coefficients and the individual's utility function. This result is obtained by using martingale techniques to reformulate the individual's dynamic optimization problem as an equivalent static one. An explicit characterization of equilibrium risk premia in the presence of portfolio constraints is also provided. In the unconstrained case, this characterization reduces to Consumption-based Capital Asset Pricing Model. (C) 1997 Academic Press.