Consistent price systems for subfiltrations
ESAIM: Probability and Statistics, Tome 11 (2007), p. 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 $\stackrel{^}{ℱ}$ 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 $\stackrel{^}{S}$ such that the price system generated by $\left(\stackrel{^}{S},Q,\stackrel{^}{ℱ}\right)$ is consistent, in a sense to be made precise, with the price system generated by $\left(S,Q,ℱ\right)$.
DOI : https://doi.org/10.1051/ps:2007004
Classification:  91B24,  93E11
@article{PS_2007__11__35_0,
author = {Gombani, Andrea and Jaschke, Stefan and Runggaldier, Wolfgang},
title = {Consistent price systems for subfiltrations},
journal = {ESAIM: Probability and Statistics},
publisher = {EDP-Sciences},
volume = {11},
year = {2007},
pages = {35-39},
doi = {10.1051/ps:2007004},
zbl = {1182.91216},
zbl = {pre05216868},
mrnumber = {2299645},
language = {en},
url = {http://www.numdam.org/item/PS_2007__11__35_0}
}

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. https://www.numdam.org/item/PS_2007__11__35_0/

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