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Martingale Representation in Progressively Enlarged Lévy Filtrations (2007.14153v1)
Published 28 Jul 2020 in math.PR
Abstract: In this paper we obtain a martingale representation theorem in the progressive enlargement $\mathbb{G}$ by a random time $\tau$ of the filtration $\mathbb{F}L$ generated by a L\'evy process $L$. The assumptions on the random time are that $\mathbb{F}^ L$ is immersed in $\mathbb{G}$ and that $\tau$ avoids $\mathbb{F}^ L$ stopping times. We also study the multiplicity of a progressively enlarged filtration.