Optimal Consumption and Equilibrium Prices with Portfolio Cone Constraints and Stochastic Labor Income

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Abstract
This paper examines the individual’s consumption and investment problem when labor income follows a general bounded process and the dollar amounts invested in the risky assets are constrained to take values in a given nonempty, closed, convex cone. Short sale constraints, as well as incomplete markets, can be modeled as special cases of this setting. Existence of optimal policies is established using martingale and duality techniques under fairly general assumptions on the security price coefficients and the individual’s utility function. This result is obtained by reformulating the individual’s dynamic optimization problem as a dual static problem over a space of martingales. 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.

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