Geodesic
Local martingales and filtration shrinkage
ESAIM: Probability and Statistics, Tome 15 (2011), pp. S25-S38

Voir la notice de l'article provenant de la source Numdam

A general theory is developed for the projection of martingale related processes onto smaller filtrations, to which they are not even adapted. Martingales, supermartingales, and semimartingales retain their nature, but the case of local martingales is more delicate, as illustrated by an explicit case study for the inverse Bessel process. This has implications for the concept of No Free Lunch with Vanishing Risk, in Finance.

DOI : 10.1051/ps/2010023
Classification : 60G44, 60H05, 60J65, 60J55
Keywords: filtration shrinkage, filtration expansion, martingales, semimartingales, local time, brownian motion 
@article{PS_2011__15__S25_0,
     author = {F\"ollmer, Hans and Protter, Philip},
     title = {Local martingales and filtration shrinkage},
     journal = {ESAIM: Probability and Statistics},
     pages = {S25--S38},
     publisher = {EDP-Sciences},
     volume = {15},
     year = {2011},
     doi = {10.1051/ps/2010023},
     mrnumber = {2817343},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2010023/}
}
TY  - JOUR
AU  - Föllmer, Hans
AU  - Protter, Philip
TI  - Local martingales and filtration shrinkage
JO  - ESAIM: Probability and Statistics
PY  - 2011
SP  - S25
EP  - S38
VL  - 15
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/ps/2010023/
DO  - 10.1051/ps/2010023
LA  - en
ID  - PS_2011__15__S25_0
ER  - 
%0 Journal Article
%A Föllmer, Hans
%A Protter, Philip
%T Local martingales and filtration shrinkage
%J ESAIM: Probability and Statistics
%D 2011
%P S25-S38
%V 15
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/ps/2010023/
%R 10.1051/ps/2010023
%G en
%F PS_2011__15__S25_0
Föllmer, Hans; Protter, Philip. Local martingales and filtration shrinkage. ESAIM: Probability and Statistics, Tome 15 (2011), pp. S25-S38. doi: 10.1051/ps/2010023

Cité par Sources :