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Second-order asymptotics for convolution of distributions with light tails

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  • Peng, Zuoxiang
  • Liao, Xin

Abstract

In this paper, asymptotic behaviors of convolutions of distributions belonging to two classes of distributions with light tails are considered. The precise second-order tail asymptotics of the convolutions are derived under the condition of second-order regular variation.

Suggested Citation

  • Peng, Zuoxiang & Liao, Xin, 2015. "Second-order asymptotics for convolution of distributions with light tails," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 199-208.
    • Handle: RePEc:eee:stapro:v:106:y:2015:i:c:p:199-208
    DOI: 10.1016/j.spl.2015.07.027
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    References listed on IDEAS

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    1. 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.
    2. Hua, Lei & Joe, Harry, 2011. "Second order regular variation and conditional tail expectation of multiple risks," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 537-546.
    3. Holger Drees, 1998. "On Smooth Statistical Tail Functionals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 187-210, March.
    4. 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.
    5. 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.
    6. Degen, Matthias & Lambrigger, Dominik D. & Segers, Johan, 2010. "Risk concentration and diversification: Second-order properties," LIDAM Reprints ISBA 2010011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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