Reflected BSDEs with regulated trajectories
  We consider reflected backward stochastic different equations with optional barrier and so-called regulated trajectories, i.e trajectories with left and right finite limits. We prove existence and uniqueness results. We also show that the solution may be approximated by a modified penalization method. Application to an optimal stopping problem is given. 
Tomasz Klimsiak, Maurycy Rzymowski, Leszek S{\l}omi\'nski
math.PR