Asymptotics for Ratios with Applications to Reinsurance

Sophie A. Ladoucette () and Jef L. Teugels ()
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Sophie A. Ladoucette: Catholic University of Leuven
Jef L. Teugels: Catholic University of Leuven

Methodology and Computing in Applied Probability, 2007, vol. 9, issue 2, 225-242

Abstract: 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.

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; Primary 60F99; Secondary 60G50, 62G20, 62G30, 62G32, 62P05 (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11009-007-9020-z

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