Before revision:  This generalizes the existing martingale representation results and does not rely on the equivalence between the conditional and the unconditional law of L . The results are illustrated in the context of hedging contingent claims under insider information.
After revision:  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.