Progressive Enlargement of Filtrations with Initial Times

Abstract

The preservation of the semi-martingale property in a progressive enlargement of filtration has been studied by many authors. Most of them focus on progressive enlargement with a honest time, allowing for semi-martingale invariance and simple decomposition formulas. However, times allowing for semi-martingale invariance in initial enlargements preserve as well this property in progressive enlargements. This paper is devoted to the related canonical decomposition of the semi-martingales. Examples are given in credit risk modelling.

Keywords: semi-martingales decomposition, filtration enlargement, initial time, credit risk

JEL Classification: C60, G13