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Consistent price systems for subfiltrations
Andrea Gombani, Stefan Jaschke, Wolfgang Runggaldier
Journal:

ESAIM: Probability and Statistics / Volume 11 / June 2007

Published online by Cambridge University Press:

01 March 2007, pp. 35-39

Print publication:

June 2007
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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).