  We deal with various alternative decompositions of F-martingales with respect
to the filtration G which represents the enlargement of a filtration F by a
progressive flow of observations of a random time that either belongs to the
class of pseudo-honest times or satisfies the extended density hypothesis.
Several related results from the existing literature are essentially extended.
Results on G-semimartingale decompositions of F-local martingales are crucial
for applications in financial mathematics, most notably in the context of
modeling credit risk and the study of insider trading where the enlargements of
filtration play a vital role. We outline two potential applications of our
results to specific problems arising in financial mathematics.
