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Consistent price systems for subfiltrations
Published online by Cambridge University Press: 01 March 2007
Abstract
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 $\hat{\mathcal F}$ 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 Ŝ such that the price system generated by (Ŝ,Q,$\hat{\mathcal F}$) is consistent, in a sense to be made precise, with the price system generated by (S,Q,F).
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- © EDP Sciences, SMAI, 2007
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