No abstract

No abstract

No abstract

In this paper, we derive the Laplace transforms of occupation times of intervals until last passage times for spectrally negative Lévy processes. Motivated by [2], the last times before an independent exponential variable are investigated here. By applying the dual argument, explicit formulas are obtained in terms of analytical identities first introduced by Loeffen et al. [13].

In this paper, we compute the Laplace transform of occupation times (of the negative half-line) of spectrally negative Lévy 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 Lévy process and its Laplace exponent. Applications to insurance risk models are also presented.