THIN-THICK APPROACH TO MARTINGALE REPRESENTATIONS ON PROGRESSIVELY ENLARGED FILTRATIONS

In this work, we investigate the propagation of the (strong) predictable representation property from a general reference filtration [Formula: see text] to its progressive enlargement with a random time [Formula: see text]. We assume that the immersion property holds, that the [Formula: see text]-thin part of [Formula: see text] is finite with positive probability, and all elements of its exhausting sequence are [Formula: see text]-predictable stopping times. In this setting, we prove a martingale representation theorem on the enlarged filtration valid across the entire time axis. Then, in light of the obtained result, we review some well-known credit risk models.