Universal state prices and asymmetric information

Abstract

This note gives a simple, robust, and arbitrage-free example of the absence of a fixed vector of state prices that applies to asymmetrically informed agents. In the same sense, the example is such that there is no universal equivalent martingale measure. The example has a finite number of agents, states, and periods. In this example, moreover, each of the asymmetrically informed agents has complete market. The example is consistent with a full rational expectations general equilibrium with learning from prices. Duffie and Huang (1986) showed conditions implying the existence of a universal equivalent martingale measure. These conditions include the assumption that one of the agents has more information than each of the others. When there is no agent whose information dominates in this sense, there is no particular reason to believe in the existence of an equivalent martingale measure (EMM) that applies to all. Our example of non-existence depends on a special information structure, as it must since prices are generically fully revealing with a finite number of states. Given this special information structure, the example is robust in that no perturbation of the payoffs of the securities allows for existence of universal state prices.