Mats Pihlsgård
	
Loss rate for Lévy processes with two reflecting barriers

Abstract:

We consider a Lévy process {X(t)} which is reflected at 0 and at some
other barrier K>0. The reflected process {VK(t)} is constructed
according to VK(t) = VK(0) + X(t) +L0(t) -LK(t), where L0(t) and LK(t)
are the local times at the respective boundaries. We define the loss
rate l(K) as the expected value in stationarity of LK(1). The
identification of l(K) in terms of characteristics of {X(t)} (the
characteristic triplet) and the stationary distribution of {VK(t)} is
the main result to be presented in the speech. I will discuss a few
simple examples in which it is possible to numerically compute l(K) and
also show a result concerning the asymptotic behaviour (as K tends to
infinity) of l(K) for a certain class of Lévy processes.