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Consistent price systems for subfiltrations

Published online by Cambridge University Press:  01 March 2007

Andrea Gombani ,
Stefan Jaschke  and
Wolfgang Runggaldier
Andrea Gombani
Affiliation:
LADSEB-CNR, Corso Stati Uniti 4, 35020 Padova, Italy; [email protected]
Stefan Jaschke
Affiliation:
BaFin, Graurheindorfer Str. 108, 53117 Bonn, Germany; [email protected]
Wolfgang Runggaldier
Affiliation:
Dipartimento Matematica Pura ed Applicata, Universitá di Padova, Via Trieste 63, 35121 Padova, Italy; [email protected]
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Abstract

Asymmetric or partial information in financial markets may berepresented by different filtrations. We consider the case of alarger filtration F – the natural filtration of the“model world” – and a subfiltration $\hat{\mathcal F}$ thatrepresents the information available to an agent in the “realworld”. Given a price system on the larger filtration that isrepresented 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 madeprecise, with the price system generated by (S,Q,F).

Keywords

Consistent price systemspartial informationnumerairefiltering.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 11: Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthdaySpecial Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday , June 2007 , pp. 35 - 39
Copyright
© EDP Sciences, SMAI, 2007

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References

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.
T. Björk, Interest rate theory, in Financial Mathematics, W.J. Runggaldier Ed., Lecture Notes in Mathematics, Springer, Berlin (1997) 53–122.
T. Björk, Arbitrage Theory in Continuous Time. Oxford University Press (1998/2004).
Brémaud, P. and Yor, M., Changes of Filtrations and of Probability Measures. Z. Wahrscheinlichkeitstheorie verw. Gebiete 45 (1978) 269–295. CrossRef
F. Delbaen and W. Schachermayer, Non-arbitrage and the fundamental theorem of asset pricing: Summary of main results. http://www.math.ethz.ch/~delbaen/. Proceedings of Symposia in Applied Mathematics of the AMS (1997).
Geman, H., El Karoui, N. and Rochet, J.-C., Changes of numéraire, changes of probability measure and option pricing. J. Appl. Probab. 32 (1995) 443–458. CrossRef
Gombani, A., Jaschke, S. and Runggaldier, W., A filtered no arbitrage model for term structures from noisy data. Stochastic Processes Appl. 115 (2005) 381–400. CrossRef