Lévy processes LOSS RATE FOR A GENERAL LÉVY PROCESS WITH DOWNWARD PERIODIC BARRIER

@inproceedings{Palmowski2011LvyPL,
  title={L{\'e}vy processes LOSS RATE FOR A GENERAL L{\'E}VY PROCESS WITH DOWNWARD PERIODIC BARRIER},
  author={Zbigniew Palmowski and PRZEMYSŁAW ŚWIA̧TEK},
  year={2011}
}
In this paper we consider a general Lévy process X reflected at a downward periodic barrier At and a constant upper barrier K , giving a process V K t = Xt + Lt − Lt . We find the expression for a loss rate defined by l = E LK1 and identify its asymptotics as K → ∞ when X has light-tailed jumps and E X1 < 0. 

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