Consistent price systems for subfiltrations

Andrea Gombani; Stefan Jaschke; Wolfgang Runggaldier

ESAIM: Probability and Statistics (2007)

  • Volume: 11, page 35-39
  • ISSN: 1292-8100

Abstract

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

How to cite

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Gombani, Andrea, Jaschke, Stefan, and Runggaldier, Wolfgang. "Consistent price systems for subfiltrations." ESAIM: Probability and Statistics 11 (2007): 35-39. <http://eudml.org/doc/250141>.

@article{Gombani2007,
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). },
author = {Gombani, Andrea, Jaschke, Stefan, Runggaldier, Wolfgang},
journal = {ESAIM: Probability and Statistics},
keywords = {Consistent price systems; partial information; numeraire; filtering.; consistent price systems; filtering},
language = {eng},
month = {3},
pages = {35-39},
publisher = {EDP Sciences},
title = {Consistent price systems for subfiltrations},
url = {http://eudml.org/doc/250141},
volume = {11},
year = {2007},
}

TY - JOUR
AU - Gombani, Andrea
AU - Jaschke, Stefan
AU - Runggaldier, Wolfgang
TI - Consistent price systems for subfiltrations
JO - ESAIM: Probability and Statistics
DA - 2007/3//
PB - EDP Sciences
VL - 11
SP - 35
EP - 39
AB - 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).
LA - eng
KW - Consistent price systems; partial information; numeraire; filtering.; consistent price systems; filtering
UR - http://eudml.org/doc/250141
ER -

References

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  6. H. Geman, N. El Karoui and J.-C. Rochet, Changes of numéraire, changes of probability measure and option pricing. J. Appl. Probab.32 (1995) 443–458.  
  7. A. Gombani, S. Jaschke and W. Runggaldier, A filtered no arbitrage model for term structures from noisy data. Stochastic Processes Appl.115 (2005) 381–400.  

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