CONSISTENT PRICE SYSTEMS FOR SUBFILTRATIONS

Asymmetric or partial information in financial markets may be represented by different nitrations. We consider the case of a larger filtration F - the natural filtration of the "model world" and a sub filtration F^ that represents the information available to an agent in the "real world". Given a price system on the larger filtration that is represented by a martingale measure Q and an associated numeraire S, we show that there is a canonical and nontrivial numeraire S^ such that the price system generated by (S^, Q^, F^?) is consistent, in a sense to be made precise, with the price system generated by (S, Q, F).