Consistent price systems for subfiltrations
LADSEB-CNR, Corso Stati Uniti 4, 35020 Padova, Italy; email@example.com
2 BaFin, Graurheindorfer Str. 108, 53117 Bonn, Germany; firstname.lastname@example.org
3 Dipartimento Matematica Pura ed Applicata, Universitá di Padova, Via Trieste 63, 35121 Padova, Italy; email@example.com
Accepted: September 2005
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 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,) is consistent, in a sense to be made precise, with the price system generated by (S,Q,F).
Mathematics Subject Classification: 91B24 / 93E11
Key words: Consistent price systems / partial information / numeraire / filtering.
© EDP Sciences, SMAI, 2007