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A property of longtailed distributions

Published online by Cambridge University Press:  14 July 2016

Paul Embrechts  and
Edward Omey
Paul Embrechts*
Affiliation:
Katholieke Universiteit, Leuven
Edward Omey*
Affiliation:
Economische Hogeschool Sint-Aloysius, Brussel
*
∗ Postal address: Department Wiskunde K. U. Leuven, Celestijnenlaan 200 B, B-3030 Leuven, Belgium.
∗∗ Postal address: Economische Hogeschool Sint-Aloysius, Broekstraat 113, B-1000 Brussel, Belgium.
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Abstract

We investigate sufficient conditions so that is subexponential. Here F is a distribution function on [0, ∞[, with finite mean. Some applications to risk theory and rates of convergence in renewal theory are given.

Keywords

INTEGRATED TAIL DISTRIBUTIONRENEWAL THEORYRISK THEORYSUBEXPONENTIALITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 1 , March 1984 , pp. 80 - 87
Copyright
Copyright © Applied Probability Trust 1984 

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References

Bingham, N. H. and Goldie, C. M. (1982) Extensions of regular variation, I: Uniformity and quantifiers. Proc. London Math. Soc. 44, 473–496.CrossRefGoogle Scholar
Chover, J., Ney, P. and Wainger, S. (1973) Functions of probability measures. J. Analyse Math. 26, 255–302.CrossRefGoogle Scholar
De Haan, L. and Resnick, S. I. (1982) Stochastic compactness and point processes. Report 8136/5, Econometric Institute, Erasmus University Rotterdam.Google Scholar
Embrechts, P. (1982) Subexponential distribution functions and their applications, A review. Proc. 7th Brasov Conf. Probability Theory. Google Scholar
Embrechts, P. and Goldie, C. M. (1980) On closure and factorisation theorems for subexponential and related distributions. J. Austral. Math. Soc. A 29, 243–256.CrossRefGoogle Scholar
Embrechts, P., Goldie, C. M. and Veraverbeke, N. (1979) Subexponentiality and infinite divisibility. Z. Wahrscheinlichkeitsth. 49, 335–347.CrossRefGoogle Scholar
Embrechts, P. and Omey, E. (1982) Functions of power series. Preprint, Leuven, K. U., Department of Mathematics.Google Scholar
Embrechts, P. and Veraverbeke, N. (1982) Estimates for the probability of ruin with special emphasis on the possibility of large claims. Insurance Math. Econom. 1, 55–72.CrossRefGoogle Scholar
Frenk, J. B. G. (1983) The behaviour of the renewal sequence in case the tail of the waiting-time distribution is regularly varying with index – 1. Adv. Appl. Prob. 14, 870–884.Google Scholar
Goldie, C. M. (1978) Subexponential distributions and dominated-variation tails. J. Appl. Prob. 15, 440–442.Google Scholar
Grübel, R. (1982) Functions of discrete probability measures: Output approximation by linear combinations of input convolution powers. Z. Wahrscheinlichkeitsth. 64, 341–357.CrossRefGoogle Scholar
Ney, P. (1981) A refinement of the coupling method in renewal theory. Stoch. Proc. Appl. 11, 11–26.CrossRefGoogle Scholar
Pakes, A. G. (1975) On the tails of waiting-time distributions. J. Appl. Prob. 12, 555–564.Google Scholar
Pitman, E. J. G. (1980) Subexponential distribution function J. Austral. Math. Soc. A 29, 337–347.CrossRefGoogle Scholar
Seneta, E. (1976) Regularly Varying Functions. Lecture Notes in Mathematics 508, Springer-Verlag, Berlin.Google Scholar
Veraverbeke, N. (1977) Asymptotic behaviour of Wiener–Hopf factors of a random walk. Stoch. Proc. Appl. 5, 27–31.Google Scholar