Loss rates for Lévy processes with two reflecting barriers

Sören Asmussen and Mats Pihlsgård

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1403-9338
Let {Xt} be a Lévy process which is reflected at 0 and K>0. The reflected process {VtK} is constructed as VtK = V0K + Xt + Lt0 - LtK where{Lt0} and {LtK} are the local times at 0 and K, respectively. We consider the loss rate lK, defined by lK=E KL1K where E K is the expectation under the stationary measure K. The main result of the paper is the identification of lK in terms of K and the characteristic triplet of {Xt}. We also derive asymptotics of lK as K when EXt <0 and the Lévy measure of {Xt} is light-tailed.
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