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Convolutions of heavy-tailed random variables and applications to portfolio diversification and MA(1) time series

Part of: Distribution theory - Probability Limit theorems

Published online by Cambridge University Press:  01 July 2016

Jaap L. Geluk ,
Liang Peng  and
Casper G. de Vries
Jaap L. Geluk*
Affiliation:
Erasmus University Rotterdam
Liang Peng*
Affiliation:
The Australian National University
Casper G. de Vries*
Affiliation:
Erasmus University Rotterdam
*
∗ Postal address: Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands. Email address: jgeluk@few.ew.nl
∗∗ Postal address: Centre for Mathematics and its Applications, The Australian National University, Canberra, ACT 0200, Australia.
∗∗∗ Postal address: Department of Economics, Erasmus University Rotterdam, 3000 DR Rotterdam, The Netherlands.
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Abstract

Suppose X1,X2 are independent random variables satisfying a second-order regular variation condition on the tail-sum and a balance condition on the tails. In this paper we give a description of the asymptotic behaviour as t → ∞ for P(X1 + X2 > t). The result is applied to the problem of risk diversification in portfolio analysis and to the estimation of the parameter in a MA(1) model.

Keywords

Heavytailsregular variationportfolio diversificationconvolutiontime series

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 60E05: Distributions
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 32 , Issue 4 , December 2000 , pp. 1011 - 1026
Copyright
Copyright © Applied Probability Trust 2000 

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