| Issue |
ESAIM: PS
Volume 11, February 2007
Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday
|
|
|---|---|---|
| Page(s) | 35 - 39 | |
| DOI | https://doi.org/10.1051/ps:2007004 | |
| Published online | 01 March 2007 | |
Consistent price systems for subfiltrations
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
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
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