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

Geluk, Jaap; Peng, Liang; Vries, Casper G. de

doi:10.1017/s0001867800010430

Cited by 11 publications

(15 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We now present an application of the above results which illustrates the difference between our result and those of Geluk et al [10]. Consider the c.d.f.…”

Section: Under the Assumptions Of Theoremsupporting

confidence: 53%

“…In a related paper Geluk et al [10] address similar problems to ours. In that paper they derive their results under an assumption of second-order regular variation.…”

Section: '-°° F(t)mentioning

confidence: 53%

“…Also very much related to the present paper, Borovkov and Borovkov [3] introduce an asymptotic differentiability condition. This condition appears to [3] Expansions for heavy tail convolutions 341 be more natural than that used by Geluk et al [10]. Equipped with this condition, Borovkov and Borovkov [3] obtained asymptotic expansions for the tail of a sum of i.i.d.…”

Section: '-°° F(t)mentioning

confidence: 91%

See 2 more Smart Citations

Asymptotic expansions of convolutions of regularly varying distributions

Barbe

McCormick²

2005

J. Aust. Math. Soc.

View full text Add to dashboard Cite

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 a semiparametric 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.2000 Mathematics subject classification: primary 62E17; secondary 62E20, 60G70.

show abstract

“…We now present an application of the above results which illustrates the difference between our result and those of Geluk et al [10]. Consider the c.d.f.…”

Section: Under the Assumptions Of Theoremsupporting

confidence: 53%

“…In a related paper Geluk et al [10] address similar problems to ours. In that paper they derive their results under an assumption of second-order regular variation.…”

Section: '-°° F(t)mentioning

confidence: 53%

Section: '-°° F(t)mentioning

confidence: 91%

See 1 more Smart Citation

Asymptotic expansions of convolutions of regularly varying distributions

Barbe

McCormick²

2005

J. Aust. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…With regard to subexponential distributions, second order work for a convolution of two such distributions may be found in Cline (1986), Cline (1987) and Geluk and Pakes (1991). We also mention that Geluk et al (2000) shows a second order result for a sum of a finite number of independent and identically distributed random variables in the special case of the underlying distribution being a member of the Hall-Weissman class. Barbe and McCormick (2005) obtained second order result for the sum of a finite number of heavy tailed random variables when the distributions also possess a mild smoothness property.…”

mentioning

confidence: 89%

Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and applications

Barbe¹,

McCormick²

2009

Memoirs of the AMS

View full text Add to dashboard Cite

show abstract

“…Further work on approximations of compound distributions in the heavy-tailed case can be found in Mikosch & Nagaev [22], Willekens [31] and Baltrūnas [5]. Higher-order asymptotic expansions were finally given in Geluk et al [18], Borovkov and Borovkov [14], Barbe and McCormick [7] and Barbe et al [11].…”

Section: Introductionmentioning

confidence: 99%

Higher-order expansions for compound distributions and ruin probabilities with subexponential claims

Albrecher

Hipp

Kortschak

2010

Scandinavian Actuarial Journal

View full text Add to dashboard Cite

Let X i (i = 1, 2, . . .) be a sequence of subexponential positive independent and identically distributed random variables. In this paper we offer two alternative approaches to obtain higher-order expansions of the tail of n i=1 X i and subsequently for ruin probabilities in renewal risk models with claim sizes X i . In particular, these emphasize the importance of the term P( n i=1 X i > s, max(X 1 , . . . , X n ) ≤ s/2) for the accuracy of the resulting asymptotic expansion of P( n i=1 X i > s). Furthermore, we present a more rigorous approach to the often suggested technique of using approximations with shifted arguments. The cases of a Pareto-type, Weibull and Lognormal distribution for X i are discussed in more detail and numerical investigations of the increase in accuracy by including higher-order terms in the approximation of ruin probabilities for finite realistic ranges of s are given.

show abstract

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

Cited by 11 publications

References 18 publications

Asymptotic expansions of convolutions of regularly varying distributions

Asymptotic expansions of convolutions of regularly varying distributions

Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and applications

Higher-order expansions for compound distributions and ruin probabilities with subexponential claims

Contact Info

Product

Resources

About