Integral representations of martingales for progressive enlargements of filtrations

DOI10.1016/J.SPA.2018.04.009zbMATH Open1488.60175arXiv1512.03992OpenAlexW2805154588WikidataQ129756434 ScholiaQ129756434MaRDI QIDQ2419970

Marek Rutkowski, Anna Aksamit, Monique Jeanblanc

Publication date: 4 June 2019

Published in: (Search for Journal in Brave)

Abstract: We work in the setting of the progressive enlargement $mathbbG$ of a reference filtration $mathbbF$ through the observation of a random time $au$. We study an integral representation property for some classes of $mathbbG$-martingales stopped at $au$. In the first part, we focus on the case where $mathbbF$ is a Poisson filtration and we establish a predictable representation property with respect to three $mathbbG$-martingales. In the second part, we relax the assumption that $mathbbF$ is a Poisson filtration and we assume that $au$ is an $mathbbF$-pseudo-stopping time. We establish integral representations with respect to some $mathbbG$-martingales built from $mathbbF$-martingales and, under additional hypotheses, we obtain a predictable representation property with respect to two $mathbbG$-martingales.

Full work available at URL: https://arxiv.org/abs/1512.03992

zbMATH Keywords

Poisson processrandom timeprogressive enlargementpredictable representation propertypseudo-stopping time

Mathematics Subject Classification ID

Stopping times; optimal stopping problems; gambling theory (60G40) Martingales with continuous parameter (60G44) Stochastic analysis (60H99)

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Related Items (5)

MARTINGALE REPRESENTATIONS IN PROGRESSIVE ENLARGEMENT BY MULTIVARIATE POINT PROCESSES ⋮ Title not available (Why is that?) ⋮ Some Remarks on Enlargement of Filtration and Finance ⋮ Integral representation of multiplicative martingale semigroups ⋮ Enlargement of filtration and predictable representation property for semi-martingales

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