 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) . This constitute our first principal (and probably the principal) innovative contribution of this paper. Our second principal contribution lies in describing and measuring the impact of \tau on log-related optimal portfolios, namely the num\'eraire portfolio and the portfolio solution to the log-utility maximization problem .
<meaning-changed>  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) . This constitute our first principal (and probably the principal) innovative contribution of this paper. Our second principal contribution lies in describing and measuring the impact of \tau on log-related optimal portfolios, namely the num\'eraire portfolio and the portfolio solution to the log-utility maximization problem .
 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) , and the case when \tau avoids \mathbb F-stopping times .