Thin-thick approach to martingale representations on progressively enlarged filtrations

Antonella Calzolari; Barbara Torti

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arXiv · 2406.08983

Thin-thick approach to martingale representations on progressively enlarged filtrations

Antonella Calzolari·Barbara Torti

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Abstract

We study the predictable representation property in the progressive enlargement F^\tau of a reference filtration F by a random time \tau. Our approach is based on the decomposition of any random time into two parts, one overlapping F-stopping times (thin part) and the other one that avoids F-stopping times (thick part). We assume that the F-thin part of \tau is nontrivial and prove a martingale representation theorem on F^\tau. We thus extend previous results dealing with F-avoiding random times. We collect some examples of application to the enlargement of the natural filtration of a L\'evy process.

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Antonella Calzolari, Barbara Torti. 2024-06-13. Thin-thick approach to martingale representations on progressively enlarged filtrations. https://arxiv.org/abs/2406.08983

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