| Issue |
ESAIM: PS
Volume 17, 2013
|
|
|---|---|---|
| Page(s) | 550 - 566 | |
| DOI | https://doi.org/10.1051/ps/2011162 | |
| Published online | 01 August 2013 | |
Carthaginian enlargement of filtrations∗
1 Scuola Normale Superiore di
Pisa, Piazza dei Cavalieri,
7
56126
Pisa,
Italy
giogiocallegaro@gmail.com
2 CREST, 15 Boulevard Gabriel Péri, 92254
Malakoff Cedex,
France
3 Institut Europlace de Finance (EIF),
Palais Brongniart, 28 Place de la
Bourse, 75002
Paris,
France
monique.jeanblanc@univ-evry.fr
4 Sharif University of
Technology, P.O. Box
11365-8639, Tehran,
Iran
behnazzargari@yahoo.com
Received:
24
January
2011
Revised:
28
September
2011
This work is concerned with the theory of initial and progressive enlargements of a
reference filtration
with a random time τ. We provide, under an
equivalence assumption, slightly stronger than the absolute continuity assumption of
Jacod, alternative proofs to results concerning canonical decomposition of an -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.
Mathematics Subject Classification: 60G46 / 60-02
Key words: Initial and progressive enlargements of filtrations / predictable projection / canonical decomposition of semimartingales / predictable representation theorem
© EDP Sciences, SMAI, 2013
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