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Modeling of claim exceedances over random thresholds for related insurance portfolios

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  • Eryilmaz, Serkan
  • Gebizlioglu, Omer L.
  • Tank, Fatih

Abstract

Large claims in an actuarial risk process are of special importance for the actuarial decision making about several issues like pricing of risks, determination of retention treaties and capital requirements for solvency. This paper presents a model about claim occurrences in an insurance portfolio that exceed the largest claim of another portfolio providing the same sort of insurance coverages. Two cases are taken into consideration: independent and identically distributed claims and exchangeable dependent claims in each of the portfolios. Copulas are used to model the dependence situations. Several theorems and examples are presented for the distributional properties and expected values of the critical quantities under concern.

Suggested Citation

  • Eryilmaz, Serkan & Gebizlioglu, Omer L. & Tank, Fatih, 2011. "Modeling of claim exceedances over random thresholds for related insurance portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 496-500.
    • Handle: RePEc:eee:insuma:v:49:y:2011:i:3:p:496-500
    DOI: 10.1016/j.insmatheco.2011.08.009
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    References listed on IDEAS

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    Cited by:

    1. Dembińska, Anna & Buraczyńska, Aneta, 2019. "The long-term behavior of number of near-maximum insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 226-237.
    2. Mohsen Bohlooli-Zefreh & Afshin Parvardeh & Majid Asadi, 2023. "On the occurrence time of an extreme damage in a general shock model," Journal of Risk and Reliability, , vol. 237(6), pages 1100-1113, December.
    3. Agah Kozan & Burak Uyar & Halil Tanil, 2024. "Exceedance statistics based on bottom- $$k$$ k -lists," Statistical Papers, Springer, vol. 65(8), pages 5239-5251, October.
    4. Erem, Aysegul & Bayramoglu, Ismihan, 2017. "Exact and asymptotic distributions of exceedance statistics for bivariate random sequences," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 181-188.

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