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Consistent price systems for subfiltrations

Published online by Cambridge University Press:  01 March 2007

Andrea Gombani ,
Stefan Jaschke  and
Wolfgang Runggaldier
Andrea Gombani
Affiliation:
LADSEB-CNR, Corso Stati Uniti 4, 35020 Padova, Italy; gombani@isib.cnr.it
Stefan Jaschke
Affiliation:
BaFin, Graurheindorfer Str. 108, 53117 Bonn, Germany; stefan@jaschke-net.de
Wolfgang Runggaldier
Affiliation:
Dipartimento Matematica Pura ed Applicata, Universitá di Padova, Via Trieste 63, 35121 Padova, Italy; runggal@math.unipd.it
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Abstract

Asymmetric or partial information in financial markets may berepresented by different filtrations. We consider the case of alarger filtration F – the natural filtration of the“model world” – and a subfiltration $\hat{\mathcal F}$ thatrepresents the information available to an agent in the “realworld”. Given a price system on the larger filtration that isrepresented 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 madeprecise, with the price system generated by (S,Q,F).

Keywords

Consistent price systemspartial informationnumerairefiltering.

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