Efficient evaluation of joint pdf of a Lévy process, its extremum, and hitting time of the extremum

Svetlana Boyarchenko, Sergei Levendorskii

For Lévy processes with exponentially decaying tails of the Lévy density, we derive integral representations for the joint cpdf $V$ of $(X_T,{\bar{X}}_T,{\tau }_T)$ (the process, its supre…