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Successive enlargement of filtrations and application to insider information

Part of: Mathematical finance Stochastic processes

Published online by Cambridge University Press:  08 September 2017

Christophette Blanchet-Scalliet ,
Caroline Hillairet  and
Ying Jiao
Christophette Blanchet-Scalliet*
Affiliation:
Université de Lyon
Caroline Hillairet*
Affiliation:
Ensae ParisTech
Ying Jiao*
Affiliation:
Université Claude Bernard - Lyon 1
*
* Postal address: Université de Lyon - CNRS, UMR 5208, Institut Camille Jordan-Ecole Centrale de Lyon, 36 avenue Guy de Collongue, 69134 Ecully Cedex, France. Email address: christophette.blanchet@ec-lyon.fr
** Postal address: CREST, UMR 9194, Ensae ParisTech, Université Paris Saclay, France. Email address: caroline.hillairet@ensae.fr
*** Postal address: Université Claude Bernard - Lyon 1, Institut de Science Financière et d'Assurances, 50 Avenue Tony Garnier, 69007 Lyon, France. Email address: ying.jiao@univ-lyon1.fr
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Abstract

We model in a dynamic way an insider's private information flow which is successively augmented by a family of initial enlargement of filtrations. According to the a priori available information, we propose several density hypotheses which are presented in hierarchical order from the weakest to the strongest. We compare these hypotheses, in particular, with Jacod's one, and deduce conditional expectations under each of them by providing consistent expressions with respect to the common reference filtration. Finally, this framework is applied to a default model with insider information on the default threshold and some numerical illustrations are performed.

Keywords

Successive enlargementdensity hypothesisinsider informationcredit risk

MSC classification

Primary: 60G99: None of the above, but in this section
Secondary: 91G40: Credit risk
Type
Research Article
Information
Advances in Applied Probability , Volume 49 , Issue 3 , September 2017 , pp. 653 - 685
Copyright
Copyright © Applied Probability Trust 2017 

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