An Insurance Risk Model with Parisian Implementation Delays

David Landriault (), Jean-François Renaud () and Xiaowen Zhou ()
Additional contact information
David Landriault: University of Waterloo
Jean-François Renaud: Université du Québec à Montréal (UQAM)
Xiaowen Zhou: Concordia University

Methodology and Computing in Applied Probability, 2014, vol. 16, issue 3, 583-607

Abstract: Abstract We consider a similar variant of the event ruin for a Lévy insurance risk process as in Czarna and Palmowski (J Appl Probab 48(4):984–1002, 2011) and Loeffen et al. (to appear, 2011) when the surplus process is allowed to spend time under a pre-specified default level before ruin is recognized. In these two articles, the ruin probability is examined when deterministic implementation delays are allowed. In this paper, we propose to capitalize on the idea of randomization and thus assume these delays are of a mixed Erlang nature. Together with the analytical interest of this problem, we will show through the development of new methodological tools that these stochastic delays lead to more explicit and computable results for various ruin-related quantities than their deterministic counterparts. Using the modern language of scale functions, we study the Laplace transform of this so-called Parisian time to ruin in an insurance risk model driven by a spectrally negative Lévy process of bounded variation. In the process, a generalization of the two-sided exit problem for this class of processes is further obtained.

Keywords: Insurance risk theory; Implementation delays; Parisian ruin; Lévy processes; Scale functions; 60G51; 91B30 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (28)

Downloads: (external link)
http://link.springer.com/10.1007/s11009-012-9317-4 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:16:y:2014:i:3:d:10.1007_s11009-012-9317-4

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

DOI: 10.1007/s11009-012-9317-4

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 ().