This paper considers an initial market model, specified by its underlying assets S and its flow of information \mathbb F, and an arbitrary random time \tau which might not be an \mathbb F-stopping time. In this setting, our principal goal resides in describing as explicit as possible the set of all deflators, which constitutes the dual set of all "admissible" wealth processes, for the stopped model S^{\tau death time and the default time (that \tau might represent) can be seen when they occur only, the progressive enlargement of \mathbb F with \tau sounds tailor-fit for modelling the new flow of information  that incorporates both \mathbb F and \tau. , \mathbb G), while the second principal goal lies in addressing the No-Free-Lunch-with-Vanishing-Risk concept (NFLVR hereafter) for (S^{\tau}, \mathbb G). Besides this direct application to NFLVR, the set of all deflators constitutes the dual set of all "admissible" wealth processes for the stopped model (S^{\tau},\mathbb G), and hence it is vital in many hedging and pricing related optimization problems. } Thanks to the deep results of Choulli et al. [ 8 ], on 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,\mathbb F), and the case when \tau avoids \mathbb F-stopping times .
This paper considers an initial market model, specified by its underlying assets S and its flow of information \mathbb F, and an arbitrary random time \tau which might not be an \mathbb F-stopping time. As the death time and the default time (that \tau might represent) can be seen when they occur only, the progressive enlargement of \mathbb F with \tau sounds tailor-fit for modelling the new flow of information \mathbb G that incorporates both \mathbb F and \tau. In this setting of informational market, the first principal goal resides in describing as explicit as possible the set of all deflators for (S^{\tau, \mathbb G), while the second principal goal lies in addressing the No-Free-Lunch-with-Vanishing-Risk concept (NFLVR hereafter) for (S^{\tau}, \mathbb G). Besides this direct application to NFLVR, the set of all deflators constitutes the dual set of all "admissible" wealth processes for the stopped model (S^{\tau},\mathbb G), and hence it is vital in many hedging and pricing related optimization problems. } Thanks to the deep results of Choulli et al. [ 7 ], on martingales classification and representation for progressive enlarged filtration, our two main goals are fully achieved in different versions, when the survival probability never vanishes . The results are illustrated on the two particular cases when ( S,\mathbb F) follows the jump-diffusion model and the discrete-time model .
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