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

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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
Keywords: consistent price systems, partial information, numeraire, filtering 
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
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     title = {Consistent price systems for subfiltrations},
     journal = {ESAIM: Probability and Statistics},
     pages = {35--39},
     year = {2007},
     publisher = {EDP-Sciences},
     volume = {11},
     doi = {10.1051/ps:2007004},
     mrnumber = {2299645},
     zbl = {1182.91216},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2007004/}
}
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