Martingale Representation in the Enlargement of the Filtration Generated by a Point Process

Paolo Di Tella, Monique Jeanblanc

Published 2019-06-04Version 1

Let $X$ be a point process and let $\mathbb{X}$ denote the filtration generated by $X$. In this paper we study the martingale representation in the filtration $\mathbb{G}$ obtained as an initial and progressive enlargement of the filtration $\mathbb{X}$. In particular, the progressive enlargement is done by means of a whole point process $H$. We work here in full generality, without requiring any further assumption on the point process $H$ and we recover the special case in which $\mathbb{X}$ is enlarged progressively by a random time $\tau$.