ESAIM: Probability and Statistics (ESAIM: P&S)

ESAIM: P&S, February 2007, Vol. 11, pp. 35-39
DOI: 10.1051/ps:2007004

Consistent price systems for subfiltrations

Andrea Gombani¹, Stefan Jaschke² and Wolfgang Runggaldier³

¹ LADSEB-CNR, Corso Stati Uniti 4, 35020 Padova, Italy; gombani@isib.cnr.it
² BaFin, Graurheindorfer Str. 108, 53117 Bonn, Germany; stefan@jaschke-net.de
³ Dipartimento Matematica Pura ed Applicata, Universitá di Padova, Via Trieste 63, 35121 Padova, Italy; runggal@math.unipd.it

(Invited paper accepted September 2005. Published online 1 March 2007.)

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

Mathematics Subject Classification. 91B24, 93E11.

Key words: Consistent price systems, partial information, numeraire, filtering.

© EDP Sciences, SMAI 2007