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Filtrations


Coculescu, D; Nikeghbali, A (2010). Filtrations. In: Cont, R. Encyclopedia of quantitative finance. Chichester, UK: John Wiley & Sons, 683-686.

Abstract

In this article, we define the notion of a filtration and the related notion of the usual hypotheses. We then explain the problem of enlargements of filtrations: how are (semi)martingales affected under a change of filtrations? We state the main theorems in the classical frameworks of initial and progressive enlargements of filtrations. In the case of initial enlargements of filtrations, we state the well known Jacod's condition and in the framework of progressive enlargements of filtrations, we give the decomposition of a local martingale in the larger filtration. We finally specialize to the case of immersed filtrations, which is very widely used in credit risk modeling, and study the effect of a combination of changes of filtration and probability measure in this situation.

Abstract

In this article, we define the notion of a filtration and the related notion of the usual hypotheses. We then explain the problem of enlargements of filtrations: how are (semi)martingales affected under a change of filtrations? We state the main theorems in the classical frameworks of initial and progressive enlargements of filtrations. In the case of initial enlargements of filtrations, we state the well known Jacod's condition and in the framework of progressive enlargements of filtrations, we give the decomposition of a local martingale in the larger filtration. We finally specialize to the case of immersed filtrations, which is very widely used in credit risk modeling, and study the effect of a combination of changes of filtration and probability measure in this situation.

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Additional indexing

Item Type:Book Section, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2010
Deposited On:14 Jan 2012 21:43
Last Modified:05 Apr 2016 15:16
Publisher:John Wiley & Sons
ISBN:978-0-470-05756-8 (P) 978-0-470-06160-2 (E)
Publisher DOI:https://doi.org/10.1002/9780470061602.eqf02011
Official URL:http://onlinelibrary.wiley.com/doi/10.1002/9780470061602.eqf02011/full

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