Volume 17, 2013
|Page(s)||550 - 566|
|Published online||01 August 2013|
Carthaginian enlargement of filtrations∗
1 Scuola Normale Superiore di
Pisa, Piazza dei Cavalieri,
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
4 Sharif University of Technology, P.O. Box 11365-8639, Tehran, Iran
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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