On the longest/shortest negative excursion of a L\'evy risk process and related quantities
Probability
2024-11-12 v1
Abstract
In this paper, we analyze some distributions involving the longest and shortest negative excursions of spectrally negative L\'evy processes using the binomial expansion approach. More specifically, we study the distributions of such excursions and related quantities such as the joint distribution of the shortest and longest negative excursion and their difference (also known as the range) over a random and infinite horizon time. Our results are applied to address new Parisian ruin problems, stochastic ordering and the number near-maximum distress periods showing the superiority of the binomial expansion approach for such cases.
Keywords
Cite
@article{arxiv.2411.06245,
title = {On the longest/shortest negative excursion of a L\'evy risk process and related quantities},
author = {M. A. Lkabous and Z. Palmowski},
journal= {arXiv preprint arXiv:2411.06245},
year = {2024}
}