Before revision:  We prove that (\rho_t)_{t \in [0,T]} can be decomposed in a pair of risk measures, acting before and after \tau and we characterize its properties giving suitable assumptions on the driver of the BSDE. Furthermore, we prove an inequality satisfied by the penalty term associated to the robust representation of (\rho_t)_{t \in [0,T]} and we provide an explicit example of such kind of dynamic risk measures, along with its decomposition .
After revision:  We prove that (\rho_t)_{t \in [0,T]} can be decomposed in a pair of risk measures, acting before and after \tau and we characterize its properties giving suitable assumptions on the driver of the BSDE. Furthermore, we prove an inequality satisfied by the penalty term associated to the robust representation of (\rho_t)_{t \in [0,T]} and we discuss the dynamic entropic risk measure case, providing examples where it is possible to write explicitly its decomposition and simulate it numerically .