Consistent price systems for subfiltrations
ESAIM: Probability and Statistics, Tome 11 (2007), pp. 35-39.

Asymmetric or partial information in financial markets may be represented by different filtrations. We consider the case of a larger filtration - 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 S ^ such that the price system generated by (S ^,Q, ^) is consistent, in a sense to be made precise, with the price system generated by (S,Q,).

DOI : 10.1051/ps:2007004
Classification : 91B24, 93E11
Mots clés : consistent price systems, partial information, numeraire, filtering
@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},
     pages = {35--39},
     publisher = {EDP-Sciences},
     volume = {11},
     year = {2007},
     doi = {10.1051/ps:2007004},
     mrnumber = {2299645},
     zbl = {1182.91216},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ps:2007004/}
}
TY  - JOUR
AU  - Gombani, Andrea
AU  - Jaschke, Stefan
AU  - Runggaldier, Wolfgang
TI  - Consistent price systems for subfiltrations
JO  - ESAIM: Probability and Statistics
PY  - 2007
SP  - 35
EP  - 39
VL  - 11
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ps:2007004/
DO  - 10.1051/ps:2007004
LA  - en
ID  - PS_2007__11__35_0
ER  - 
%0 Journal Article
%A Gombani, Andrea
%A Jaschke, Stefan
%A Runggaldier, Wolfgang
%T Consistent price systems for subfiltrations
%J ESAIM: Probability and Statistics
%D 2007
%P 35-39
%V 11
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ps:2007004/
%R 10.1051/ps:2007004
%G en
%F 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. http://www.numdam.org/articles/10.1051/ps:2007004/

[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. | Zbl

[3] T. Björk, Arbitrage Theory in Continuous Time. Oxford University Press (1998/2004). | Zbl

[4] P. Brémaud and M. Yor, Changes of Filtrations and of Probability Measures. Z. Wahrscheinlichkeitstheorie verw. Gebiete 45 (1978) 269-295. | Zbl

[5] F. Delbaen and W. Schachermayer, Non-arbitrage and the fundamental theorem of asset pricing: Summary of main results1997). | MR | Zbl

[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. | Zbl

[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.

Cité par Sources :