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Progressive Enlargements of Filtrations with Pseudo-Honest Times and their Applications in Financial Mathematics

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.