On the Devylder–Goovaerts Conjecture in Ruin Theory

Stéphane Loisel () and Charles Minier
Additional contact information
Stéphane Loisel: Laboratoire de Sciences Actuarielle et Financière, Institut de Science Financière et d’Assurances, Université Claude Bernard Lyon 1, Univ Lyon, 50 Avenue Tony Garnier, F-69007 Lyon, France
Charles Minier: Laboratoire de Sciences Actuarielle et Financière, Institut de Science Financière et d’Assurances, Université Claude Bernard Lyon 1, Univ Lyon, 50 Avenue Tony Garnier, F-69007 Lyon, France

Mathematics, 2023, vol. 11, issue 6, 1-10

Abstract: The Devylder–Goovaerts conjecture is probably the oldest conjecture in actuarial mathematics and has received a lot of attention in recent years. It claims that ruin with equalized claim amounts is always less likely than in the classical model. Investigating the validity of this conjecture is important both from a theoretical aspect and a practical point of view, as it suggests that one always underestimates the risk of insolvency by replacing claim amounts with the average claim amount a posteriori. We first state a simplified version of the conjecture in the discrete-time risk model when one equalizes aggregate claim amounts and prove that it holds. We then use properties of the Pareto distribution in risk theory and other ideas to target candidate counterexamples and provide several counterexamples to the original Devylder–Goovaerts conjecture.

Keywords: ruin theory; Devylder–Goovaerts conjecture; equalized claim amounts; applied probability; insurance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/6/1501/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/6/1501/ (text/html)

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:gam:jmathe:v:11:y:2023:i:6:p:1501-:d:1101784

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().