Integral representations of martingales for progressive enlargements of filtrations

Anna Aksamit , Monique Jeanblanc , Marek Rutkowski

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.
Author Anna Aksamit
Anna Aksamit,,
-
, Monique Jeanblanc
Monique Jeanblanc,,
-
, Marek Rutkowski (FMIS / DSPFM) - [The University of Sydney]
Marek Rutkowski,,
- Department of Stochastic Processes and Financial Mathematics
- The University of Sydney
Journal seriesStochastic Processes and Their Applications, ISSN 0304-4149, (A 25 pkt)
Issue year2019
Vol129
No4
Pages1229-1258
Publication size in sheets1.45
Keywords in EnglishPredictable representation property; Poisson process; Random time; Progressive enlargement; Pseudo-stopping time
ASJC Classification2604 Applied Mathematics; 2611 Modelling and Simulation; 2613 Statistics and Probability
DOIDOI:10.1016/j.spa.2018.04.009
URL https://www.sciencedirect.com/science/article/pii/S0304414918301406
Languageen angielski
Score (nominal)25
ScoreMinisterial score = 25.0, 08-07-2019, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2017 = 1.177; WoS Impact Factor: 2017 = 1.051 (2) - 2017=1.277 (5)
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