Occupation times of intervals until first passage times for spectrally negative L\'evy processes

TL;DR

This paper derives explicit formulas for occupation times of intervals until first passage times in spectrally negative Lévy processes, with applications to finance and insurance risk modeling.

Contribution

It introduces new analytical identities for scale functions, enabling explicit expressions for occupation times in spectrally negative Lévy processes.

Findings

Explicit Laplace transforms of occupation times derived

New identities for scale functions established

Applications demonstrated in option pricing and insurance risk

Abstract

In this paper, we identify Laplace transforms of occupation times of intervals until first passage times for spectrally negative L\'evy processes. New analytical identities for scale functions are derived and therefore the results are explicitly stated in terms of the scale functions of the process. Applications to option pricing and insurance risk models are also presented.