Asymmetric or partial information in financial markets may be
represented by different filtrations. We consider the case of a
larger filtration F – the natural filtration of the
“model world” – and a subfiltration $\hat{\mathcal F}$ 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 Ŝ such that the price system generated by
(Ŝ,Q,$\hat{\mathcal F}$) is consistent, in a sense to be made
precise, with the price system generated by (S,Q,F).