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Asymptotics for Ratios with Applications to Reinsurance |
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| Authors: | Sophie A. Ladoucette Jef L. Teugels |
| Affiliation: | (1) Department of Mathematics, Catholic University of Leuven, W. de Croylaan 54, 3001 Leuven, Belgium;(2) EURANDOM, Technical University of Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands |
| Abstract: | This paper provides an overview of results pertaining to moment convergence for certain ratios of random variables involving sums, order statistics and extreme terms in the sense of modulus. Most of the literature on this matter originates from Darling (1952) who gave a criterion for the convergence in probability to 1 of the ratio of the maximum to the sum in case of nonnegative random variables. Sophie A. Ladoucette is supported by the grant BDB-B/04/03 of the Catholic University of Leuven. |
| Keywords: | Limit theorems Functions of regular variation Domain of attraction of a stable law Order statistics Sum of i.i.d. random variables Dominance of summands Moments |
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