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This paper considers an initial market model, specified by its underlyingassets $S$ and its flow of information $\mathbb F$, and an arbitrary randomtime $\tau$ which might not be an $\mathbb F$-stopping time. As the death timeand the default time (that $\tau$ might represent) can be seen when they occuronly, the progressive enlargement of $\mathbb F$ with $\tau$ sounds tailor-fitfor modelling the new flow of information $\mathbb G$ that incorporates both$\mathbb F$ and $\tau$. In this setting of informational market, the firstprincipal goal resides in describing as explicitly as possible the set of alldeflators for $(S^{\tau}, \mathbb G)$, while the second principal goal lies inaddressing the No-Free-Lunch-with-Vanishing-Risk concept (NFLVR hereafter) for$(S^{\tau}, \mathbb G)$. Besides this direct application to NFLVR, the set ofall deflators constitutes the dual set of all "admissible" wealth processes forthe stopped model $(S^{\tau},\mathbb G)$, and hence it is vital in many hedgingand pricing related optimization problems. Thanks to the results of Choulli etal. [7], on martingales classification and representation for progressiveenlarged filtration, our two main goals are fully achieved in differentversions, when the survival probability never vanishes. The results areillustrated on the two particular cases when $(S,\mathbb F)$ follows thejump-diffusion model and the discrete-time model.

Explicit description of all deflators for market models under random horizon with applications to NFLVR