Integral representations of martingales for progressive enlargements of filtrations

Anna Aksamit, Monique Jeanblanc and Marek Rutkowski

Stochastic Processes and their Applications, 2019, vol. 129, issue 4, 1229-1258

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

Keywords: Predictable representation property; Poisson process; Random time; Progressive enlargement; Pseudo-stopping time (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:129:y:2019:i:4:p:1229-1258

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DOI: 10.1016/j.spa.2018.04.009

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