On the Propagation of the Weak Representation Property in Independently Enlarged Filtrations: The General Case

2020/03/25 by Di Tella, Paolo
#60G44 #60G57 #60H05 #60H30 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2003.11636

Abstract

In this paper we investigate the propagation of the weak representation property (WRP) to an independently enlarged filtration. More precisely, we consider an \mathbbF-semimartingale X possessing the WRP with respect to \mathbbF and an ℍ-semimartingale Y possessing the WRP with respect to ℍ. Assuming that \mathbbF and ℍ are independent, we show that the \mathbbG-semimartingale Z=(X,Y) has the WRP with respect to \mathbbG, where \mathbbG:=\mathbbF\veeℍ. In our setting, X and Y may have simultaneous jump-times. Furthermore, their jumps may charge predictable times. This generalizes all available results about the propagation of the WRP to independently enlarged filtrations.

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