Consumption and Portfolio Policies With Incomplete Markets and Short‐Sale Constraints: the Finite‐Dimensional Case¹

We use a martingale approach to study optimal intertemporal consumption and portfolio policies in a general discrete‐time, discrete‐state‐space securities market with dynamically incomplete markets and short‐sale constraints. We characterize the set of feasible consumption bundles as the budget‐feasible set defined by constraints formed using the extreme points of the closure of the set of Arrow‐Debreu state prices consistent with no arbitrage, and then establish a relationship between the original problem and a dual minimization problem.