Carthaginian enlargement of filtrations

Giorgia Callegaro; Monique Jeanblanc; Behnaz Zargari

ESAIM: Probability and Statistics (2013)

  • Volume: 17, page 550-566
  • ISSN: 1292-8100

Abstract

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This work is concerned with the theory of initial and progressive enlargements of a reference filtration 𝔽 F with a random timeτ. We provide, under an equivalence assumption, slightly stronger than the absolute continuity assumption of Jacod, alternative proofs to results concerning canonical decomposition of an 𝔽 F -martingale in the enlarged filtrations. Also, we address martingales’ characterization in the enlarged filtrations in terms of martingales in the reference filtration, as well as predictable representation theorems in the enlarged filtrations.

How to cite

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Callegaro, Giorgia, Jeanblanc, Monique, and Zargari, Behnaz. "Carthaginian enlargement of filtrations." ESAIM: Probability and Statistics 17 (2013): 550-566. <http://eudml.org/doc/273629>.

@article{Callegaro2013,
abstract = {This work is concerned with the theory of initial and progressive enlargements of a reference filtration $\mathbb \{F\}$ F with a random timeτ. We provide, under an equivalence assumption, slightly stronger than the absolute continuity assumption of Jacod, alternative proofs to results concerning canonical decomposition of an $\mathbb \{F\}$ F -martingale in the enlarged filtrations. Also, we address martingales’ characterization in the enlarged filtrations in terms of martingales in the reference filtration, as well as predictable representation theorems in the enlarged filtrations.},
author = {Callegaro, Giorgia, Jeanblanc, Monique, Zargari, Behnaz},
journal = {ESAIM: Probability and Statistics},
keywords = {initial and progressive enlargements of filtrations; predictable projection; canonical decomposition of semimartingales; predictable representation theorem; initial and progressive enlargement of filtrations; predictable representation; change of probability measure},
language = {eng},
pages = {550-566},
publisher = {EDP-Sciences},
title = {Carthaginian enlargement of filtrations},
url = {http://eudml.org/doc/273629},
volume = {17},
year = {2013},
}

TY - JOUR
AU - Callegaro, Giorgia
AU - Jeanblanc, Monique
AU - Zargari, Behnaz
TI - Carthaginian enlargement of filtrations
JO - ESAIM: Probability and Statistics
PY - 2013
PB - EDP-Sciences
VL - 17
SP - 550
EP - 566
AB - This work is concerned with the theory of initial and progressive enlargements of a reference filtration $\mathbb {F}$ F with a random timeτ. We provide, under an equivalence assumption, slightly stronger than the absolute continuity assumption of Jacod, alternative proofs to results concerning canonical decomposition of an $\mathbb {F}$ F -martingale in the enlarged filtrations. Also, we address martingales’ characterization in the enlarged filtrations in terms of martingales in the reference filtration, as well as predictable representation theorems in the enlarged filtrations.
LA - eng
KW - initial and progressive enlargements of filtrations; predictable projection; canonical decomposition of semimartingales; predictable representation theorem; initial and progressive enlargement of filtrations; predictable representation; change of probability measure
UR - http://eudml.org/doc/273629
ER -

References

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