  We study the optimal stopping problem for dynamic risk measures represented
by Backward Stochastic Differential Equations (BSDEs) with jumps and its
relation with reflected BSDEs (RBSDEs). We first provide general existence,
uniqueness and comparison theorems for RBSDEs with jumps in the case of a RCLL
adapted obstacle. We then show that the value function of the optimal stopping
problem is characterized as the solution of an RBSDE.
  The existence of an optimal stopping time is obtained when the obstacle is
left-upper semi-continuous along stopping times. Finally, robust optimal
stopping problems related to the case with model ambiguity are investigated.
