Before revision:  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).
After revision:  In this setting of informational market, the first principal goal resides in describing as explicitly 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).