On the last exit times for spectrally negative L\'evy processes

TL;DR

This paper introduces a novel method to derive joint Laplace transforms for spectrally negative Lévy processes, focusing on last exit times, process values, and occupation times, thereby extending existing theoretical results.

Contribution

The paper presents a new approach to compute joint Laplace transforms involving last exit times, generalizing previous findings for spectrally negative Lévy processes.

Findings

Derived joint Laplace transforms for last exit times and related quantities

Generalized previous results in the theory of spectrally negative Lévy processes

Provided a new analytical framework for exit time analysis

Abstract

Using a new approach, for spectrally negative L\'evy processes we find joint Laplace transforms involving the last exit time (from a semi-infinite interval), the value of the process at the last exit time and the associated occupation time, which generalizes some previous results.