Imperfect Information Leads to Complete Markets if Dividends are Diffusions

A pure exchange economy with a financial market is studied where aggregate dividends are modeled as a diffusion. The dynamics of the diffusion are allowed to depend on factors which are unobservable to the agents and have to be estimated. With perfect information, the asset market would be incomplete because there are more factors than traded assets. Imperfect information reduces the number of observable risks, but also the number of admissible portfolio strategies. It is shown that, as long as the observable dividend stream is a diffusion, the asset market is complete. It is therefore possible to establish the existence of an equilibrium with dynamically complete markets that leads to the same allocation as the Arrow-Debreu equilibrium.