Loss rates for levy processes with two reflecting barriers

We consider a Levy process that is reflected at 0 and at K > 0. The reflected process is obtained by adding the difference between the local time at 0 and the local time at K to the sum of the feeding Levy process and an initial condition. We define the loss rate to be the expectation of the local time at K at time I under stationary conditions. The main result of the paper is the identification of the loss rate in terms of the stationary measure of the reflected process and the characteristic triplet of the Levy process. We also derive asymptotics of the loss rate as K -> infinity when the drift of the feeding process is negative and the Levy measure is light tailed. Finally, we extend the results for Levy processes to hold for Markov-modulated Levy processes.