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 …

The last couple of years has seen a remarkable number of new, explicit examples of the
Wiener–Hopf factorization for Lévy processes where previously there had been very few. We …

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 …

We develop a completely new and straightforward method for simulating the joint law of the
position and running maximum at a fixed time of a general Lévy process with a view to …

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 …

We examine discounted penalties at ruin for surplus dynamics driven by a general spectrally
negative Lévy process; the natural class of stochastic processes which contains many …

The drawdown process Y of a completely asymmetric Lévy process X is equal to X reflected
at its running supremum X¯: Y= X¯− X. In this paper we explicitly express in terms of the …

We consider the spectrally negative Lévy processes and determine the joint laws for the
quantities such as the first and last passage times over a fixed level, the overshoots and …