Progressive enlargements of filtrations with pseudo-honest times

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 revisited and essentially extended. Results on G-semimartingale decompositions of F-local martingales are crucial for applications in financial mathematics, most notably in the context of credit risk modeling and the study of insider trading where the enlarged filtration plays a vital role. We outline potential applications of our results to problems arising in financial mathematics.