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On the Monotone Stability Approach to BSDEs with Jumps: Extensions, Concrete Criteria and Examples Read chapter Read first chapter

2019 | OriginalPaper | Chapter

An Example of Martingale Representation in Progressive Enlargement by an Accessible Random Time

Authors : Antonella Calzolari, Barbara Torti

Published in: Frontiers in Stochastic Analysis–BSDEs, SPDEs and their Applications

Publisher: Springer International Publishing

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Abstract

Given two martingales on the same probability space, both enjoying the predictable representation property with respect to their own filtrations, it can happens that their quadratic covariation process enters in the martingale representation of the filtration obtained as the union of the original ones. This fact on one hand influences the multiplicity of the enlarged filtration and on the other hand it is linked to the behavior of the sharp brackets of the martingales. Here we illustrate these arguments presenting an elementary example of martingale representation in the context of progressive enlargement by an accessible random time.

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Metadata
Title
An Example of Martingale Representation in Progressive Enlargement by an Accessible Random Time
Authors
Antonella Calzolari
Barbara Torti
Copyright Year
2019
Book
Frontiers in Stochastic Analysis–BSDEs, SPDEs and their Applications

Print ISBN: 978-3-030-22284-0

Electronic ISBN: 978-3-030-22285-7

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-22285-7_4