# Consistent price systems for subfiltrations

Andrea Gombani; Stefan Jaschke; Wolfgang Runggaldier

ESAIM: Probability and Statistics (2007)

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

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topGombani, 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

top- M. Atlan, H. Geman, D.B. Madan and M. Yor, Correlation and the pricing of risks. Prépublications du Laboratoire de Probabilités et Modèles Aléatoires (2004), No. 877. Zbl1233.91320
- T. Björk, Interest rate theory, in Financial Mathematics, W.J. Runggaldier Ed., Lecture Notes in Mathematics, Springer, Berlin (1997) 53–122. Zbl0904.90007
- T. Björk, Arbitrage Theory in Continuous Time. Oxford University Press (1998/2004). Zbl1140.91038
- P. Brémaud and M. Yor, Changes of Filtrations and of Probability Measures. Z. Wahrscheinlichkeitstheorie verw. Gebiete45 (1978) 269–295. Zbl0415.60048
- F. Delbaen and W. Schachermayer, Non-arbitrage and the fundamental theorem of asset pricing: Summary of main results. . Proceedings of Symposia in Applied Mathematics of the AMS (1997). Zbl0969.91004URIhttp://www.math.ethz.ch/~delbaen/
- 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. Zbl0829.90007
- 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. Zbl1151.91510

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