Martingale representation property in progressively enlarged filtrations

Details Martingale representation property in progressively enlarged filtrations Martingale representation property in progressively enlarged filtrations

2012-03-07

arxiv.org/abs/1203.1447v1

Mathematics

Probability

Scientific paper

Consider $\mathbb{G}$ the progressive enlargement of a filtration $\mathbb{F}$ with a random time $\tau$. Assuming that, in $\mathbb{F}$, the martingale representation property holds, we examine conditions under which the martingale representation property holds also in $\mathbb{G}$. It is noted that the classical results on this subject are no more sufficient to deal with all examples coming from credit risk modeling. In this paper, we introduce a new methodology which extends the various classical results and applies on recent examples.

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