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 ] martingales classification and representation for progressive enlarged filtration, our aim is fully achieved for both cases of local martingale deflators and general supermartingale delators. The results are illustrated on several particular models for (\tau,S,\mathbb F) such as the discrete-time and the jump-diffusion settings for (S ^{\tau,\mathbb G) in terms of the deflators of the initial market model (S} ,\mathbb F) .