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On the stop-loss and total variation distances between random sums

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  • Denuit, Michel
  • Van Bellegem, Sébastien

Abstract

The purpose of this work is to provide upper bounds on the stop-loss and total variation distances between random sums. The main theoretical argument consists in defining discrete analogs of the classical ideal metrics considered by Rachev and Rüschendorf (Adv. Appl. Probab. 22 (1990) 350). An application in risk theory enhances the relevance of the approach proposed in this paper.

Suggested Citation

  • Denuit, Michel & Van Bellegem, Sébastien, 2001. "On the stop-loss and total variation distances between random sums," Statistics & Probability Letters, Elsevier, vol. 53(2), pages 153-165, June.
    • Handle: RePEc:eee:stapro:v:53:y:2001:i:2:p:153-165
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    References listed on IDEAS

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    1. Gerber, Hans U., 1984. "Error bounds for the compound poisson approximation," Insurance: Mathematics and Economics, Elsevier, vol. 3(3), pages 191-194, July.
    2. De Pril, Nelson & Dhaene, Jan, 1992. "Error Bounds for Compound Poisson Approximations of the Individual Risk Model," ASTIN Bulletin, Cambridge University Press, vol. 22(2), pages 135-148, November.
    3. Kaas, R. & Gerber, H. U., 1994. "Some alternatives for the individual model," Insurance: Mathematics and Economics, Elsevier, vol. 15(2-3), pages 127-132, December.
    4. Vellaisamy, P. & Chaudhuri, B., 1999. "On compound Poisson approximation for sums of random variables," Statistics & Probability Letters, Elsevier, vol. 41(2), pages 179-189, January.
    5. Denuit, Michel & Lefevre, Claude, 1997. "Some new classes of stochastic order relations among arithmetic random variables, with applications in actuarial sciences," Insurance: Mathematics and Economics, Elsevier, vol. 20(3), pages 197-213, October.
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