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An asymptotic expansion for the tail of compound sums of Burr distributed random variables

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  • Kortschak, Dominik
  • Albrecher, Hansjörg

Abstract

In this paper we show that it is possible to write the Laplace transform of the Burr distribution as the sum of four series. This representation is then used to provide a complete asymptotic expansion of the tail of the compound sum of Burr distributed random variables. Furthermore it is shown that if the number of summands is fixed, this asymptotic expansion is actually a series expansion if evaluated at sufficiently large arguments.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:7-8:p:612-620
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    References listed on IDEAS

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    1. Geluk, J. L., 1992. "Second order tail behaviour of a subordinated probability distribution," Stochastic Processes and their Applications, Elsevier, vol. 40(2), pages 325-337, March.
    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. Albrecher, Hansjörg & Kortschak, Dominik, 2009. "On ruin probability and aggregate claim representations for Pareto claim size distributions," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 362-373, December.
    4. 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.
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    Cited by:

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    2. Nguyen Quang Huy & Robert Christian Y., 2015. "Series expansions for convolutions of Pareto distributions," Statistics & Risk Modeling, De Gruyter, vol. 32(1), pages 49-72, April.

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