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Enlargement of Filtration in Discrete Time

  • Christophette Blanchet-ScallietEmail author
  • Monique Jeanblanc
Chapter
  • 27 Downloads
Part of the Mathematical Lectures from Peking University book series (MLPKU)

Abstract

In this lecture, we study enlargement of filtration in a discrete time setting. In a discrete time setting, considering two filtrations \({\mathbb F}\) and \({\mathbb G}\) with \({\mathbb F}\subset {\mathbb G}\), any \({\mathbb F}\)-martingale is a \({\mathbb G}\)-semimartingale. We give the decomposition of \({\mathbb F}\)-martingales in \({\mathbb G}\)-semimartingales in the case of initial (and progressive) enlargement. We study progressive enlargement with pseudo-stopping times and honest times.

Keywords

Enlargement of filtration Initial enlargement Progressive enlargement Azéma’s supermartingale Discrete time Doob decomposition Pseudo-stopping times Honest times 

Mathematics Subject Classification (2010)

60G05 60G42 60G99 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Christophette Blanchet-Scalliet
    • 1
    Email author
  • Monique Jeanblanc
    • 2
  1. 1.Université de Lyon - CNRS, UMR 5208, Institut Camille Jordan - Ecole Centrale de LyonEcully CedexFrance
  2. 2.LaMME, UMR CNRS 8071, Univ Evry, Université Paris SaclayEvryFrance

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