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

TL;DR

This paper investigates how enlarging filtrations with pseudo-honest times affects martingale decompositions, with applications to credit risk modeling and insider trading in financial mathematics.

Contribution

It extends existing results on filtration enlargements by pseudo-honest times and provides new G-semimartingale decomposition techniques for financial applications.

Findings

Extended decomposition results for F-martingales under enlarged filtrations.

Applications demonstrated in credit risk and insider trading models.

New theoretical tools for modeling information flow in finance.

Abstract

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.