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 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, ℱ ^ ) 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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  1. 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.  
  2. T. Björk, Interest rate theory, in Financial Mathematics, W.J. Runggaldier Ed., Lecture Notes in Mathematics, Springer, Berlin (1997) 53–122.  
  3. T. Björk, Arbitrage Theory in Continuous Time. Oxford University Press (1998/2004).  
  4. P. Brémaud and M. Yor, Changes of Filtrations and of Probability Measures. Z. Wahrscheinlichkeitstheorie verw. Gebiete45 (1978) 269–295.  
  5. 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).  URIhttp://www.math.ethz.ch/~delbaen/
  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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