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On ruin probability and aggregate claim representations for Pareto claim size distributions

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  • Albrecher, Hansjörg
  • Kortschak, Dominik
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    Abstract

    We generalize an integral representation for the ruin probability in a Crámer-Lundberg risk model with shifted (or also called US-)Pareto claim sizes, obtained by Ramsay (2003), to classical Pareto(a) claim size distributions with arbitrary real values a>1 and derive its asymptotic expansion. Furthermore an integral representation for the tail of compound sums of Pareto-distributed claims is obtained and numerical illustrations of its performance in comparison to other aggregate claim approximations are provided.

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 45 (2009)
    Issue (Month): 3 (December)
    Pages: 362-373

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    Handle: RePEc:eee:insuma:v:45:y:2009:i:3:p:362-373

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    Web page: http://www.elsevier.com/locate/inca/505554

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    1. Embrechts, P. & Veraverbeke, N., 1982. "Estimates for the probability of ruin with special emphasis on the possibility of large claims," Insurance: Mathematics and Economics, Elsevier, vol. 1(1), pages 55-72, January.
    2. Ramsay, Colin M., 2003. "A solution to the ruin problem for Pareto distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 109-116, August.
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    Cited by:
    1. Kortschak, Dominik & Albrecher, Hansjörg, 2010. "An asymptotic expansion for the tail of compound sums of Burr distributed random variables," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 612-620, April.
    2. Hansjoerg Albrecher & Corina Constantinescu & Stéphane Loisel, 2011. "Explicit ruin formulas for models with dependence among risks," Post-Print hal-00540621, HAL.

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