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Let $X$ be a point process and let $\mathbb{X}$ denote the filtrationgenerated by $X$. In this paper we study martingale representation theorems inthe filtration $\mathbb{G}$ obtained as an initial and progressive enlargementof the filtration $\mathbb{X}$. The progressive enlargement is done here bymeans of a whole point process $H$. We do not require further assumptions onthe point process $H$ nor on the dependence between $X$ and $H$. In particular,we recover the special case of the progressive enlargement by a random time$\tau$.

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