Asymptotic expansions of convolutions of regularly varying distributions
Open Access
- 9 April 2005
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 78 (3) , 339-371
Abstract
In this paper we derive precise tail-area approximations for the sum of an arbitrary finite number of independent heavy-tailed random variables. In order to achieve second-order asymptotics, a mild regularity condition is imposed on the class of distribution functions with regularly varying tails.Higher-order asymptotics are also obtained when considering asemiparametric subclass of distribution functions with regularly varying tails. These semiparametric subclasses are shown to be closed under convolutions and a convolution algebra is constructed to evaluate the parameters of a convolution from the parameters of the constituent distributions in the convolution. A Maple code is presented which does this task.Keywords
This publication has 12 references indexed in Scilit:
- On Probabilities of Large Deviations for Random Walks. I. Regularly Varying Distribution TailsTheory of Probability & Its Applications, 2002
- Lundberg Approximations for Compound Distributions with Insurance Applications2001
- Convolutions of heavy-tailed random variables and applications to portfolio diversification and MA(1) time seriesAdvances in Applied Probability, 2000
- Convolutions of heavy-tailed random variables and applications to portfolio diversification and MA(1) time series2000
- On the estimation of extreme tail probabilitiesThe Annals of Statistics, 1997
- Modelling Extremal Events1997
- Regular Variation1987
- Extreme Values, Regular Variation and Point Processes1987
- Point processes, regular variation and weak convergenceAdvances in Applied Probability, 1986
- On convolution tailsStochastic Processes and their Applications, 1982