| 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
This email address is being protected from spambots. You need JavaScript enabled to view it.
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
This email address is being protected from spambots. You need JavaScript enabled to view it.
4 Sharif University of
Technology, P.O. Box
11365-8639, Tehran,
Iran
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Received:
24
January
2011
Revised:
28
September
2011
Abstract
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
This research was supported by the “Chaire Risque de Crédit” of the French Banking Federation. All the authors are members of the Université d’Evry Val d’Essonne, Laboratoire d’Analyse et Probabilités, 23 Boulevard de France, 91037 Evry cedex, France.
© EDP Sciences, SMAI, 2013
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