The purpose of this review article is to give an up to date account of the theory and
applications of scale functions for spectrally negative Lévy processes. Our review also …

Lévy processes are the natural continuous-time analogue of random walks and form a rich
class of stochastic processes around which a robust mathematical theory exists. Their …

Lévy processes are the natural continuous-time analogue of random walks and form a rich
class of stochastic processes around which a robust mathematical theory exists. Their …

After having worked in the domain of Gaussian queues for about a decade, we got the idea
to look at similar problems, but now in the context of Lévy-driven queues. That step felt as …

In this paper we introduce a ten-parameter family of Lévy processes for which we obtain
Wiener–Hopf factors and distribution of the supremum process in semi-explicit form. This …

In this paper we study the optimal dividend problem for a company whose surplus process
evolves as a spectrally positive Lévy process before dividends are deducted. This model …

Stable Lévy processes lie at the intersection of Lévy processes and self-similar Markov
processes. Processes in the latter class enjoy a Lamperti-type representation as the space …

We study the distribution and various properties of exponential functionals of
hypergeometric Lévy processes. We derive an explicit formula for the Mellin transform of the …

In our previous publications (IJTAF 2019, Math. Finance 2020), we introduced a general
class of SINH-regular processes and demonstrated that efficient numerical methods for the …

We clarify the relations among different Fourier-based approaches to option pricing, and
improve the B-spline probability density projection method using the sinh-acceleration …