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Second order behaviour of the tail of a subordinated probability distribution

Author

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  • Omey, E.
  • Willekens, E.

Abstract

Let G = [Sigma][infinity]n=0pnF*n denote the probability measure subordinate to F with subordinator {Pn}. We investigate the asymptotic behaviour of (1 - G(x))-([Sigma] npn)(1 - F(x)) as x --> [infinity] if 1 - F is regularly varying with index [varrho], 0

Suggested Citation

  • Omey, E. & Willekens, E., 1986. "Second order behaviour of the tail of a subordinated probability distribution," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 339-353, February.
    • Handle: RePEc:eee:spapps:v:21:y:1986:i:2:p:339-353
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    Citations

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    Cited by:

    1. Omey, Edward & Vesilo, R., 2009. "Random Sums of Random Variables and Vectors," Working Papers 2009/09, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
    2. Geluk, J. L., 1996. "Tails of subordinated laws: The regularly varying case," Stochastic Processes and their Applications, Elsevier, vol. 61(1), pages 147-161, January.
    3. Lin, Jianxi, 2012. "Second order asymptotics for ruin probabilities in a renewal risk model with heavy-tailed claims," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 422-429.
    4. Bikramjit Das & Marie Kratz, 2017. "Diversification benefits under multivariate second order regular variation," Working Papers hal-01520655, HAL.
    5. Toshiro Watanabe, 2022. "Second-Order Behaviour for Self-Decomposable Distributions with Two-Sided Regularly Varying Densities," Journal of Theoretical Probability, Springer, vol. 35(2), pages 1343-1366, June.
    6. Jianxi Lin, 2012. "Second order Subexponential Distributions with Finite Mean and Their Applications to Subordinated Distributions," Journal of Theoretical Probability, Springer, vol. 25(3), pages 834-853, September.
    7. Søren Asmussen & Jaakko Lehtomaa, 2017. "Distinguishing Log-Concavity from Heavy Tails," Risks, MDPI, vol. 5(1), pages 1-14, February.
    8. Degen, Matthias & Lambrigger, Dominik D. & Segers, Johan, 2010. "Risk concentration and diversification: Second-order properties," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 541-546, June.
    9. Mitov, Kosto V. & Omey, Edward, 2014. "Intuitive approximations for the renewal function," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 72-80.
    10. Das, Bikramjit & Kratz, Marie, 2017. "Diversification benefits under multivariate second order regular variation," ESSEC Working Papers WP1706, ESSEC Research Center, ESSEC Business School.
    11. Barbe, Ph. & McCormick, W.P. & Zhang, C., 2007. "Tail expansions for the distribution of the maximum of a random walk with negative drift and regularly varying increments," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1835-1847, December.
    12. Gareth W. Peters & Rodrigo S. Targino & Pavel V. Shevchenko, 2013. "Understanding Operational Risk Capital Approximations: First and Second Orders," Papers 1303.2910, arXiv.org.
    13. Lorenzo Hern'andez & Jorge Tejero & Alberto Su'arez & Santiago Carrillo-Men'endez, 2012. "Percentiles of sums of heavy-tailed random variables: Beyond the single-loss approximation," Papers 1203.2564, arXiv.org, revised Dec 2012.
    14. Geluk, J. & de Haan, L. & Resnick, S. & Starica, C., 1997. "Second-order regular variation, convolution and the central limit theorem," Stochastic Processes and their Applications, Elsevier, vol. 69(2), pages 139-159, September.

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