Consistent price systems for subfiltrations
ESAIM: Probability and Statistics, Tome 11 (2007), pp. 35-39.

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 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 S ^ such that the price system generated by (S ^,Q,ℱ ^) is consistent, in a sense to be made precise, with the price system generated by (S,Q,ℱ).

DOI : 10.1051/ps:2007004
Classification : 91B24, 93E11
Mots-clés : consistent price systems, partial information, numeraire, filtering 
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Gombani, Andrea; Jaschke, Stefan; Runggaldier, Wolfgang. Consistent price systems for subfiltrations. ESAIM: Probability and Statistics, Tome 11 (2007), pp. 35-39. doi : 10.1051/ps:2007004. http://www.numdam.org/articles/10.1051/ps:2007004/

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