Local martingales and filtration shrinkage

Hans Föllmer; Philip Protter

ESAIM: Probability and Statistics (2011)

  • Volume: 15, page S25-S38
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Föllmer, Hans, and Protter, Philip. "Local martingales and filtration shrinkage." ESAIM: Probability and Statistics 15 (2011): S25-S38. <http://eudml.org/doc/277146>.

@article{Föllmer2011,
abstract = {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.},
author = {Föllmer, Hans, Protter, Philip},
journal = {ESAIM: Probability and Statistics},
keywords = {filtration shrinkage; filtration expansion; martingales; semimartingales; local time; brownian motion},
language = {eng},
pages = {S25-S38},
publisher = {EDP-Sciences},
title = {Local martingales and filtration shrinkage},
url = {http://eudml.org/doc/277146},
volume = {15},
year = {2011},
}

TY - JOUR
AU - Föllmer, Hans
AU - Protter, Philip
TI - Local martingales and filtration shrinkage
JO - ESAIM: Probability and Statistics
PY - 2011
PB - EDP-Sciences
VL - 15
SP - S25
EP - S38
AB - 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.
LA - eng
KW - filtration shrinkage; filtration expansion; martingales; semimartingales; local time; brownian motion
UR - http://eudml.org/doc/277146
ER -

References

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