Thin-thick approach to martingale representations on progressively enlarged filtrations
Probability
2024-06-21 v2
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.
Keywords
Cite
@article{arxiv.2406.08983,
title = {Thin-thick approach to martingale representations on progressively enlarged filtrations},
author = {Antonella Calzolari and Barbara Torti},
journal= {arXiv preprint arXiv:2406.08983},
year = {2024}
}