  We study the strong predictable representation property in filtrations
initially enlarged with a random variable L. We prove that the strong
predictable representation property can always be transferred to the enlarged
filtration as long as the classical density hypothesis of Jacod (1985) holds.
This generalizes the existing martingale representation results and does not
rely on the equivalence between the conditional and the unconditional laws of
L. Depending on the behavior of the density process at zero, different forms of
martingale representation are established. The results are illustrated in the
context of hedging contingent claims under insider information.
