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,
2005
ISSN 14039338

Abstract:

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 lighttailed.



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