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.
Mots clés : 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://archive.numdam.org/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://archive.numdam.org/articles/10.1051/ps/2010023/ DO - 10.1051/ps/2010023 LA - en ID - PS_2011__15__S25_0 ER -
Föllmer, Hans; Protter, Philip. Local martingales and filtration shrinkage. ESAIM: Probability and Statistics, Tome 15 (2011), pp. S25-S38. doi : 10.1051/ps/2010023. http://archive.numdam.org/articles/10.1051/ps/2010023/
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