Informational Efficiency with Trading Constraints : A Characterization

Given a market with a price process S populated by heterogeneous traders with differential information, beliefs, and trading constraints, let the smallest information set containing all of the traders' information be denoted F. This market is defined to be informationally efficient (Fama [2]) with respect to an information set G ⊆ F if the price process S arises as an outcome of a competitive market equilibrium. We provide a characterization of such an informationally efficient market. Roughly stated, a market is informationally efficient with respect to G if and only if there exists an equivalent probability measure that makes the price process normalized by the value of a money market account a martingale with respect to G if and only if the market satisfies no free lunch with vanishing risk (NFLVR) and no dominance (ND) with respect G. This characterization subsumes the economies and characterizations contained in the more restrictive market settings of Jarrow and Larsson [7, 8]