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

Michel Denuit, Christian Genest and Étienne Marceau

Scandinavian Actuarial Journal, 2002, vol. 2002, issue 1, 3-16

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.

Date: 2002
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DOI: 10.1080/03461230110106192

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