We present a robust method for simulating an increment of a Levy process, based on
decomposing the jump part of the process into the sum of its positive and negative jump …

The simulation of a discrete sample path of a Levy process reduces to simulating from the
distribution of a Levy increment. For a general Levy process with exponential moments, the …

The simulation of a discrete sample path of a Lévy process reduces to simulating from the
distribution of a Lévy increment. For a general Lévy process with exponential moments, the …

In this paper, we present an iterative procedure to calculate explicitly the Laplace transform
of the distribution of the maximum for a Lévy process with positive jumps of phase type. We …

Lévy processes have found applications in various fields, including physics, chemistry, long-
term climate change, telephone communication, and finance. The most famous Lévy …

In this extended abstract we propose a method to estimate the parameters of the
characteristic function of a Lévy Process. It is designed to eliminate computational problems …

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 present a robust numerical method to compute the scale function W (q)(x) of
a general spectrally negative Lévy process (X, P). The method is based on the Esscher …

The one–and two-dimensional normal inverse Gaussian Lévy process is studied in relation
to German and Danish financial data. In order to investigate if the normal inverse Gaussian …

This dissertation is divided into two parts: the first part is a literature review and the second
describes three new contributions to the literature. The literature review aims to provide a …