Integral representations of martingales for progressive enlargements of filtrations
Anna Aksamit , Monique Jeanblanc , Marek Rutkowski
AbstractWe 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.
|Journal series||Stochastic Processes and Their Applications, ISSN 0304-4149, (A 25 pkt)|
|Publication size in sheets||1.45|
|Keywords in English||Predictable representation property; Poisson process; Random time; Progressive enlargement; Pseudo-stopping time|
|ASJC Classification||; ;|
|Score||= 25.0, 08-07-2019, ArticleFromJournal|
|Publication indicators||: 2017 = 1.177; : 2017 = 1.051 (2) - 2017=1.277 (5)|
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