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On some compound distributions with Borel summands

Author

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  • Finner, H.
  • Kern, P.
  • Scheer, M.

Abstract

The generalized Poisson distribution is well known to be a compound Poisson distribution with Borel summands. As a generalization we present closed formulas for compound Bartlett and Delaporte distributions with Borel summands and a recursive structure for certain compound shifted Delaporte mixtures with Borel summands. Our models are introduced in an actuarial context as claim number distributions and are derived only with probabilistic arguments and elementary combinatorial identities. In the actuarial context related compound distributions are of importance as models for the total size of insurance claims for which we present simple recursion formulas of Panjer type.

Suggested Citation

  • Finner, H. & Kern, P. & Scheer, M., 2015. "On some compound distributions with Borel summands," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 234-244.
    • Handle: RePEc:eee:insuma:v:62:y:2015:i:c:p:234-244
    DOI: 10.1016/j.insmatheco.2015.03.012
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    References listed on IDEAS

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    1. Goovaerts, M. J. & Kaas, R., 1991. "Evaluating Compound Generalized Poisson Distributions Recursively," ASTIN Bulletin, Cambridge University Press, vol. 21(2), pages 193-198, November.
    2. Gerber, Hans U., 1990. "When does the surplus reach a given target?," Insurance: Mathematics and Economics, Elsevier, vol. 9(2-3), pages 115-119, September.
    3. Paul Embrechts & Marco Frei, 2009. "Panjer recursion versus FFT for compound distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 497-508, July.
    4. Ruohonen, Matti, 1988. "On A Model for the Claim Number Process," ASTIN Bulletin, Cambridge University Press, vol. 18(1), pages 57-68, April.
    5. Willmot, Gordon E., 1989. "Limiting tail behaviour of some discrete compound distributions," Insurance: Mathematics and Economics, Elsevier, vol. 8(3), pages 175-185, November.
    6. Panjer, Harry H., 1981. "Recursive Evaluation of a Family of Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 12(1), pages 22-26, June.
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