We introduce a family of bivariate discrete distributions whose members are generated by a decreasing mass function <italic>p</italic>, and with margins given by <italic>p</italic>. Several properties and examples are obtained, including a family of seemingly novel bivariate Poisson distributions.

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...

In this paper, we identify Laplace transforms of occupation times of intervals until first passage times for spectrally negative Lévy processes. New analytical identities for scale functions are derived and therefore the results are explicitly stated in terms of the scale functions of the...

We study the distribution of tax payments in the model of Kyprianou and Zhou [Kyprianou, A.E., Zhou, X., 2009. General tax structures and the Lévy insurance risk model. J. Appl. Probab. (in press)], that is a Lévy insurance risk model with a surplus-dependent tax rate. More precisely, after a...

In a Lévy insurance risk model, under the assumption that the tail of the Lévy measure is log-convex, we show that either a horizontal barrier strategy or the take-the-money-and-run strategy maximizes, among all admissible strategies, the dividend payments subject to an affine penalty function...