  We define a class of reflected backward stochastic differential equation
(RBSDE) driven by a marked point process (MPP) and a Brownian motion, where the
solution is constrained to stay above a given c\`adl\`ag process. The MPP is
only required to be non-explosive and to have totally inaccessible jumps. Under
suitable assumptions on the coefficients we obtain existence and uniqueness of
the solution, using the Snell envelope theory. We use the equation to represent
the value function of an optimal stopping problem, and we characterize the
optimal strategy.
  Keywords: reflected backward stochastic differential equations, optimal
stopping, marked point processes.
