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Joint asymptotic distributions of smallest and largest insurance claims

Author

Listed:
  • Hansjörg Albrecher
  • Christian Y. Robert

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Jef L. Teugels

Abstract

. Assume that claims in a portfolio of insurance contracts are described by independent and identically distributed random variables with regularly varying tails and occur according to a near mixed Poisson process. We provide a collection of results pertaining to the joint asymptotic Laplace transforms of the normalized sums of the smallest and largest claims, when the length of the considered time interval tends to infinity. The results crucially depend on the value of the tail index of the claim distribution, as well as on the number of largest claims under consideration.

Suggested Citation

  • Hansjörg Albrecher & Christian Y. Robert & Jef L. Teugels, 2014. "Joint asymptotic distributions of smallest and largest insurance claims," Post-Print hal-01294387, HAL.
    • Handle: RePEc:hal:journl:hal-01294387
    DOI: 10.3390/risks2030289
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    Cited by:

    1. Albrecher, Hansjörg & García Flores, Brandon, 2022. "Asymptotic analysis of generalized Greenwood statistics for very heavy tails," Statistics & Probability Letters, Elsevier, vol. 185(C).
    2. Søren Asmussen & Jaakko Lehtomaa, 2017. "Distinguishing Log-Concavity from Heavy Tails," Risks, MDPI, vol. 5(1), pages 1-14, February.

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