Occupation times of spectrally negative Lévy processes with applications

David Landriault, Jean-François Renaud, Xiaowen Zhou

Published 2010-12-15, updated 2011-05-04Version 3

In this paper, we compute the Laplace transform of occupation times (of the negative half-line) of spectrally negative L\'evy processes. Our results are extensions of known results for standard Brownian motion and jump-diffusion processes. The results are expressed in terms of the so-called scale functions of the spectrally negative L\'evy process and its Laplace exponent. Applications to insurance risk models are also presented.