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.Journal of Economic LiteratureClassification Numbers: G11, G12, C61, D52, D91.
* This is a revised version of the second chapter of my doctoral dissertation at the University of California at Berkeley. Financial support from the Haas School of Business is gratefully acknowledged. I thank Hua He and JakImage a CvitaniImage for several conversations on this topic and Darrell Duffie, Christina Shannon, Jiang Wang, Fernando Zapatero, and seminar participants at the Courant Institute, the Massachusetts Institute of Technology, Northwestern University, the University of Pennsylvania, the Instituto Tecnologico Autonomo de Mexico (ITAM), the 1995 meeting of the Western Finance Association, the 1995 meeting of the European Finance Association, the 1995 INFORMS Applied Probability Conference, and the 1996 CIRANO/CRM Workshop on the Mathematics of Finance for comments. JakImage a CvitaniImage pointed out a mistake in an early version of this paper. I am of course solely responsible for any remaining errors.