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On the Devylder–Goovaerts Conjecture in Ruin Theory

Author

Listed:
  • 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)

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.

Suggested Citation

  • Stéphane Loisel & Charles Minier, 2023. "On the Devylder–Goovaerts Conjecture in Ruin Theory," Mathematics, MDPI, vol. 11(6), pages 1-10, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1501-:d:1101784
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    References listed on IDEAS

    as
    1. Christian Yann Robert, 2014. "On the De Vylder and Goovaerts Conjecture About Ruin for Equalized Claims," Post-Print hal-02006620, HAL.
    2. Stefan Ankirchner & Christophette Blanchet-Scalliet & Nabil Kazi-Tani, 2019. "The De Vylder-Goovaerts conjecture holds true within the diffusion limit," Post-Print hal-01887402, HAL.
    3. De Vylder, F. & Goovaerts, M., 2000. "Homogeneous risk models with equalized claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 223-238, May.
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