Integral representations of martingales for progressive enlargements of filtrations.

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. [ABSTRACT FROM AUTHOR]