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De Vylder and Goovaerts' conjecture on homogeneous risk models with equalized claim amounts

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  • Kim, Bara
  • Kim, Jeongsim
  • Kim, Jerim

Abstract

De Vylder and Goovaerts (2000) made a conjecture on the comparison of the finite time ruin probability in a homogeneous risk model and the corresponding ruin probability in an associated model with equalized claim amounts. The conjecture, however, remains an open problem. In this paper, we provide a conjecture that is stronger than De Vylder and Goovaerts' conjecture and also provide sufficient conditions for the conjectures, which are more mathematically tractable than De Vylder and Goovaerts' conjecture and thus easier to work with. By using the sufficient conditions for the conjectures, we solve De Vylder and Goovaerts' conjecture when n=3, where n is the number of claims in the finite time.

Suggested Citation

  • Kim, Bara & Kim, Jeongsim & Kim, Jerim, 2021. "De Vylder and Goovaerts' conjecture on homogeneous risk models with equalized claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 186-201.
    • Handle: RePEc:eee:insuma:v:101:y:2021:i:pb:p:186-201
    DOI: 10.1016/j.insmatheco.2021.07.007
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    References listed on IDEAS

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    1. Christian Yann Robert, 2014. "On the De Vylder and Goovaerts Conjecture About Ruin for Equalized Claims," Post-Print hal-02006620, HAL.
    2. De Vylder, F. E. & Goovaerts, M. J., 1999. "Inequality extensions of Prabhu's formula in ruin theory," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 249-271, May.
    3. Lefèvre, Claude & Picard, Philippe, 2011. "A new look at the homogeneous risk model," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 512-519.
    4. 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.
    5. 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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    More about this item

    Keywords

    De Vylder and Goovaerts' conjecture; Homogeneous risk model; Ruin probability; Risk reserve process; Order statistics;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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