Work

On the longest/shortest negative excursion of a Lévy risk process and related quantities

Year: 2024

Type: article

Abstract: In this paper, we analyze some distributions involving the longest and shortest negative excursions of spectrally negative Lévy 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 excursions 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.

Source: Scandinavian Actuarial Journal

DOI: 10.1080/03461238.2024.2424273

Authors: M. A. Lkabous, Z. Palmowski

Institutions: University of Southampton, Wrocław University of Science and Technology

Language: English

Topic: Probability and Risk Models

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: hybrid

Funders: University of Southampton, Narodowe Centrum Nauki

Award: G678311281