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Criteria for the Stochastic Ordering of Random Sums, with Actuarial Applications

Author

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  • Michel Denuit
  • Christian Genest
  • Étienne Marceau

Abstract

It is shown that vectors ( S M 1 , … , S Mn ) and ( S' M'1 , …, S' M'n ) of random sums of positive random variables are stochastically ordered by upper orthant dependence, lower orthant dependence, concordance or by the supermodular ordering whenever their corresponding random numbers of terms ( M 1 , … , M n ) and ( M' 1 , … , M' n ) are themselves ordered in this fashion. Actuarial applications of these results are given to different dependence structures for the collective risk model with several classes of business.

Suggested Citation

  • Michel Denuit & Christian Genest & Étienne Marceau, 2002. "Criteria for the Stochastic Ordering of Random Sums, with Actuarial Applications," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2002(1), pages 3-16.
  • Handle: RePEc:taf:sactxx:v:2002:y:2002:i:1:p:3-16
    DOI: 10.1080/03461230110106192
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