On occupation times in the red of L\'evy risk models
Abstract
In this paper, we obtain analytical expression for the distribution of the occupation time in the red (below level ) up to an (independent) exponential horizon for spectrally negative L\'{e}vy risk processes and refracted spectrally negative L\'{e}vy risk processes. This result improves the existing literature in which only the Laplace transforms are known. Due to the close connection between occupation time and many other quantities, we provide a few applications of our results including future drawdown, inverse occupation time, Parisian ruin with exponential delay, and the last time at running maximum. By a further Laplace inversion to our results, we obtain the distribution of the occupation time up to a finite time horizon for refracted Brownian motion risk process and refracted Cram\'{e}r-Lundberg risk model with exponential claims.
Keywords
Cite
@article{arxiv.1903.03721,
title = {On occupation times in the red of L\'evy risk models},
author = {David Landriault and Bin Li and Mohamed Amine Lkabous},
journal= {arXiv preprint arXiv:1903.03721},
year = {2019}
}