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 $$\bar{X}_t:= \sup _{0\le s\le t} X_s$$ denoting the running...

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>