Gombani, Andrea; Jaschke, Stefan; Runggaldier, Wolfgang
Consistent price systems for subfiltrations
ESAIM: Probability and Statistics, Tome 11 (2007) , p. 35-39
Zbl pre05216868 | MR 2299645
doi : 10.1051/ps:2007004
URL stable : http://www.numdam.org/item?id=PS_2007__11__35_0

Classification:  91B24,  93E11
Asymmetric or partial information in financial markets may be represented by different filtrations. We consider the case of a larger filtration - 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 S ^ such that the price system generated by (S ^,Q, ^) is consistent, in a sense to be made precise, with the price system generated by (S,Q,).

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