Before revision:  Thanks to the deep results of Choulli et al (2016) on the ] martingales classification and representation for progressive enlarged filtration, we completely and explicitly describe all the deflators for (S ^{\tau,\mathbb G) in terms of the deflators of the initial market model (S} ,\mathbb F) .
After revision:  Thanks to the deep results of Choulli et al (2016) on the ], on martingales classification and representation for progressive enlarged filtration, we completely and explicitly describe all the deflators for (S ^{\tau,\mathbb G) in terms of the deflators of the initial market model (S} ,\mathbb F) .