Consistent price systems for subfiltrations
Asymmetric or partial information in financial markets may be represented by different filtrations. We consider the case of a larger filtration – the natural filtration of the “model world” – and a subfiltration 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 and an associated numeraire , we show that there is a canonical and nontrivial numeraire Ŝ such that the price system...