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Maxima of Sums of Heavy-Tailed Random Variables

Published online by Cambridge University Press:  29 August 2014

K.W. Ng ,
Q.H. Tang  and
H. Yang
K.W. Ng
Affiliation:
Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulatn Road, Hong Kong, E-mail:kaing@hku.hk
Q.H. Tang
Affiliation:
University of Amsterdam, Department of Quantitative Economics, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands, E-mail:tangqihe@263.net
H. Yang
Affiliation:
Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong, E-mail:hlyang@hku.hk
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Abstract

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In this paper, we investigate asymptotic properties of the tail probabilities of the maxima of partial sums of independent random variables. For some large classes of heavy-tailed distributions, we show that the tail probabilities of the maxima of the partial sums asymptotically equal to the sum of the tail probabilities of the individual random variables. Then we partially extend the result to the case of random sums. Applications to some commonly used risk processes are proposed. All heavy-tailed distributions involved in this paper are supposed on the whole real line.

Keywords

AsymptoticsHeavy tailsInsurance risk modelPartial sumsRandom sumsSubexponential distributionTail probabilities
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 32 , Issue 1 , May 2002 , pp. 43 - 55
Copyright
Copyright © International Actuarial Association 2002

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