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Mathematics
Article . 2023 . Peer-reviewed
License: CC BY
Data sources: Crossref
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Mathematics
Article . 2023
Data sources: DOAJ
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On the Devylder–Goovaerts Conjecture in Ruin Theory

Authors: Stéphane Loisel; Charles Minier;

On the Devylder–Goovaerts Conjecture in Ruin Theory

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, ruin theory; Devylder–Goovaerts conjecture; equalized claim amounts; applied probability; insurance, QA1-939, equalized claim amounts, applied probability, Mathematics, insurance

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Top 10%
Average
gold