This paper focuses on numerical evaluation techniques related to fluctuation theory for Lévy processes; they can be applied in various domains, e.g., in finance in the pricing of so-called barrier options. More specifically, with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\bar{X}_t:= \sup _{0\le s\le t} X_s$$</EquationSource> </InlineEquation> denoting the running...</equationsource></inlineequation>

For prices of options with barrier and lookback features, defaultable bonds and credit default swaps (CDSs), and probability distribution functions in Lévy models, as well as for joint probability distributions of a Lévy process and its supremum or/and infimum, one can derive explicit...

In the paper, we propose two new efficient methods for pricing barrier option in wide classes of Lévy processes with/without regime switching. Both methods are based on the numerical Laplace transform inversion formulae and the Fast Wiener-Hopf factorization method developed in Kudryavtsev and...

This short communication considers a tandem queue fed by Lévy input. The main result concerns expressions for the Laplace transform of the transient workload in the downstream queue, under the condition that the system starts off empty. This expression greatly simplifies if the driving Lévy...

In this paper, we describe two computational methods for calculating the cumulative distribution function and the upper quantiles of the maximal difference between a Brownian bridge and its concave majorant. The first method has two different variants that are both based on a Monte Carlo...