Gerber-Shiu Function for a Class of Markov-Modulated Lévy Risk Processes with Two-Sided Jumps

Ehyter Matías Martín-González (), Antonio Murillo-Salas () and Henry Pantí ()
Additional contact information
Ehyter Matías Martín-González: Universidad de Guanajuato
Antonio Murillo-Salas: Universidad de Guanajuato
Henry Pantí: Universidad Autónoma de Yucatán

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 4, 2779-2800

Abstract: Abstract We investigate the Gerber-Shiu discounted penalty function for Markov-modulated Lévy risk processes with random incomes. Firstly, we consider the case when the downward and upward jumps (respectively, claims and random gains) are given by independent compound Poisson processes, with claim sizes with a general distribution function and gains in such a way that their distribution has a rational Laplace transform. Afterwards, we use the above results and weak convergence techniques to study the case when the claims are given by a subordinator and, subsequently, we establish results when the claims are governed by a pure spectrally positive Lévy jump process. Some numerical examples are presented in order to illustrate our results.

Keywords: Gerber-Shiu function; Lévy risk processes; Markov-modulated processes; Subordinator; Spectrally positive Lévy processes; Random gains; Risk processes in random environments; 60G51; 60J75; 60K37; 91B30 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-022-09954-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:24:y:2022:i:4:d:10.1007_s11009-022-09954-1

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-022-09954-1

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().