Criteria for the Stochastic Ordering of Random Sums,with Actuarial Applications |
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| Authors: | Michel Denuit Christian Genest Étienne Marceau |
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| Institution: | Institute of Mathematics , University of Oslo , Blindern, Oslo 3 , Norway |
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| 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. |
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| Keywords: | Adjustment Coefficient Collective Risk Model Comonotonicity Concordance Copulas Lower Orthant Dependence Positive Quadrant Dependence Upper Orthant Dependence Random Sums Supermodular Ordering |
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