Before revision:  To solve this problem, we provide a connection between the dynamic convex risk functional introduced and the solutionof a quadratic RBSDE (Reflected Backward Stochastic Differential Equations): this is achieved by studying the properties of specific non linear expectations  .
After revision:  To solve this problem, we provide a connection between the dynamic convex risk functional introduced and the solutionof a quadratic RBSDE (Reflected Backward Stochastic Differential Equations): this is achieved by studying the properties of specific non linear expectations , has again the time consistency property .