In this paper, we prove the existence and uniqueness of the solution to reflected backward doubly stochastic differential equations driven by Teugels martingales associated with a L\'evy process where the barrier process is not necessarily right continuous by approximating such equations by a new version of penalization method.
A note on first passage probabilities of a Lévy process reflected at a general barrier
Efficient evaluation of expectations of functions of a Lévy process and its extremum
Zooming-in on a Lévy process: Failure to observe threshold exceedance over a dense grid
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