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Carthaginian enlargement of filtrations∗

Published online by Cambridge University Press:  01 August 2013

Giorgia Callegaro ,
Monique Jeanblanc  and
Behnaz Zargari
Giorgia Callegaro
Affiliation:
Scuola Normale Superiore di Pisa, Piazza dei Cavalieri, 7 56126 Pisa, Italy. [email protected] CREST, 15 Boulevard Gabriel Péri, 92254 Malakoff Cedex, France
Monique Jeanblanc
Affiliation:
Institut Europlace de Finance (EIF), Palais Brongniart, 28 Place de la Bourse, 75002 Paris, France; [email protected]
Behnaz Zargari
Affiliation:
Sharif University of Technology, P.O. Box 11365-8639, Tehran, Iran; [email protected]
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Abstract

This work is concerned with the theory of initial and progressive enlargements of a reference filtration \hbox{$\mathbb{F}$}F 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 \hbox{$\mathbb{F}$}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.

Keywords

Initial and progressive enlargements of filtrationspredictable projectioncanonical decomposition of semimartingalespredictable representation theorem
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 17 , 2013 , pp. 550 - 566
Copyright
© EDP Sciences, SMAI, 2013

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