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Asymptotics for Ratios with Applications to Reinsurance

Author

Listed:
  • Sophie A. Ladoucette

    (Catholic University of Leuven)

  • Jef L. Teugels

    (Catholic University of Leuven
    Technical University of Eindhoven)

Abstract

This paper provides an overview of results pertaining to moment convergence for certain ratios of random variables involving sums, order statistics and extreme terms in the sense of modulus. Most of the literature on this matter originates from Darling (1952) who gave a criterion for the convergence in probability to 1 of the ratio of the maximum to the sum in case of nonnegative random variables.

Suggested Citation

  • Sophie A. Ladoucette & Jef L. Teugels, 2007. "Asymptotics for Ratios with Applications to Reinsurance," Methodology and Computing in Applied Probability, Springer, vol. 9(2), pages 225-242, June.
    • Handle: RePEc:spr:metcap:v:9:y:2007:i:2:d:10.1007_s11009-007-9020-z
    DOI: 10.1007/s11009-007-9020-z
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    References listed on IDEAS

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    1. Smid, B. & Stam, A. J., 1975. "Convergence in distribution of quotients of order statistics," Stochastic Processes and their Applications, Elsevier, vol. 3(3), pages 287-292, July.
    2. Ladoucette, Sophie A., 2007. "Asymptotic behavior of the moments of the ratio of the random sum of squares to the square of the random sum," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 1021-1033, June.
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    Cited by:

    1. Arvydas Astrauskas, 2023. "Some Bounds for the Expectations of Functions on Order Statistics and Their Applications," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1116-1147, June.
    2. Hansjörg Albrecher & Christian Y. Robert & Jef L. Teugels, 2014. "Joint Asymptotic Distributions of Smallest and Largest Insurance Claims," Risks, MDPI, vol. 2(3), pages 1-26, July.

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