J.L. Geluk
http://repub.eur.nl/ppl/37/
List of Publicationsenhttp://repub.eur.nl/eur_logo.png
http://repub.eur.nl/
RePub, Erasmus University RepositoryWeak & Strong Financial Fragility
http://repub.eur.nl/pub/8747/
Wed, 14 Feb 2007 00:00:01 GMT<div>J.L. Geluk</div><div>L.F.M. de Haan</div><div>C.G. de Vries</div>
The stability of the financial system at higher loss levels is either characterized by asymptotic dependence or asymptotic independence. If asymptotically independent, the dependency, when present, eventually dies out completely at the more extreme quantiles, as in case of the multivariate normal distribution. Given that financial service firms' equity returns depend linearly on the risk drivers, we show that the marginals' distributions maximum domain of attraction determines the type of systemic (in-)stability. A scale for the amount of dependency at high loss lovels is designed. This permits a characterization of systemic risk inherent to different financial network structures. The theory also suggests the functional form of the economically relevant limit copulas.Weighted sums of subexponential random variables and asymptotic dependence between returns on reinsurance equities
http://repub.eur.nl/pub/12370/
Fri, 24 Feb 2006 00:00:01 GMT<div>J.L. Geluk</div><div>C.G. de Vries</div>
Suppose $X_1, X_2, \\ldots$ are independent subexponential random variables with
partial sums $S_n$. We show that if the pairwise sums of the $X_i$’s are
subexponential, then $S_n$ is subexponential and $(S_n > x) ∼ \\sum_{i}^n P(X_i
> x)(x \\rightarrow \\infty)$. The result is applied to give
conditions under which $P(\\sum_{1}^\\infty c_iX_i > x)$ as $x \\rightarrow
\\infty$, where $c_1, c_2, \\ldots$ are constants such that $\\sum_{1}^\\infty
c_iX_i$ is a.s. convergent. Asymptotic tail probabilities for bivariate linear combinations of subexponential random variables are given. These results are applied to explain the joint movements of the stocks of reinsurers. Portfolio investment and retrocession practices in the reinsurance industry expose different reinsurers to the same subexponential risks on both sides of their balance sheets. This implies that reinsurer’s equity returns can be asymptotically dependent, exposing the industry to systemic risk.Weighted sums of subexponential random variables and asymptotic dependence between returns on reinsurance equities
http://repub.eur.nl/pub/1800/
Fri, 05 Nov 2004 00:00:01 GMT<div>J.L. Geluk</div><div>C.G. de Vries</div>
Asymptotic tail probabilities for bivariate linear combinations of subexponential random variables are given. These results are applied to explain the joint movements of the stocks of reinsurers. Portfolio investment and retrocession practices in the reinsurance industry, for reasons of diversification, exposes different reinsurers to the same risks on both sides of their balance sheets. Assuming, in line with the industry practice that the risk drivers follow subexponential distributions, we derive (under mild conditions) when the reinsurer's equity returns are asymptotically dependent, exposing the industry to systemic risk.Weighted Sums of Subexponential Random Variables and Asymptotic Dependence between Returns on Reinsurance Equities
http://repub.eur.nl/pub/6615/
Sun, 12 Sep 2004 00:00:01 GMT<div>J.L. Geluk</div><div>C.G. de Vries</div>
Asymptotics in the symmetrization inequality
http://repub.eur.nl/pub/66546/
Sun, 01 Aug 2004 00:00:01 GMT<div>J.L. Geluk</div>
We give a sufficient condition for i.i.d. random variables X1,X2 in order to have P{X1 -X2>x}∼P{ X1 >x}, as x→∞. A factorization property for subexponential distributions is used in the proof.Asymptotics in the symmetrization inequality
http://repub.eur.nl/pub/1055/
Thu, 07 Aug 2003 00:00:01 GMT<div>J.L. Geluk</div>
We give a sufficient condition for i.i.d. random variables
X1,X2 in order to have P{X1-X2>x} ~ P{|X1|>x}
as x tends to infinity. A factorization property for
subexponential distributions is used in the proof. In a subsequent
paper the results will be applied to model fragility of financial
markets.On bootstrap sample size in extreme value theory
http://repub.eur.nl/pub/541/
Mon, 11 Nov 2002 00:00:01 GMT<div>J.L. Geluk</div><div>L.F.M. de Haan</div>
It has been known for a long time that for bootstrapping the
probability distribution of the maximum of a sample consistently,
the bootstrap sample size needs to be of smaller order than the
original sample size. See Jun Shao and Dongsheng Tu (1995), Ex.
3.9,p. 123. We show that the same is true if we use the bootstrap
for estimating an intermediate quantile.Convolutions of heavy-tailed random variables and applications to portfolio diversification and MA(1) time series
http://repub.eur.nl/pub/54286/
Fri, 01 Dec 2000 00:00:01 GMT<div>J.L. Geluk</div><div>L. Peng</div><div>C.G. de Vries</div>
Convolutions of heavy-tailed random variables and applications to portfolio diversification and MA(1) time series
http://repub.eur.nl/pub/12390/
Sat, 01 Jan 2000 00:00:01 GMT<div>J.L. Geluk</div><div>L. Peng</div><div>C.G. de Vries</div>
Convolutions of Heavy Tailed Random Variables and Applications to Portfolio Diversification and MA(1) Time Series
http://repub.eur.nl/pub/7711/
Thu, 14 Oct 1999 00:00:01 GMT<div>J.L. Geluk</div><div>L. Peng</div><div>C.G. de Vries</div>
The paper characterizes first and second order tail behavior of convolutions of i.i.d. heavy tailed random variables with support on the real line. 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.An adaptive optimal estimate of the tail index for MA(1) time series
http://repub.eur.nl/pub/1564/
Tue, 30 Mar 1999 00:00:01 GMT<div>J.L. Geluk</div><div>L. Peng</div>
For samples of random variables with a regularly varying tail estimating the tail index has received much attention recently.
For the proof of asymptotic normality of the tail index estimator second order regular variation is needed. In this paper we first supplement earlier results on convolution given by Geluk et al. (1997). Secondly we propose a simple estimator of the tail index for finite moving average time series. We also give a subsampling procedure in order to estimate the optimal sample fraction in the sense of minimal mean squared error.Second order regular variation and the domain of attraction of stable distributions
http://repub.eur.nl/pub/1547/
Thu, 13 Aug 1998 00:00:01 GMT<div>J.L. Geluk</div><div>L. Peng</div>
We characterize second order regular variation of the tail sum of F together with a balance condition on the tails interms of the behaviour of the characteristic function near zero.Stable Probability Distributions and their Domains of Attraction
http://repub.eur.nl/pub/7796/
Fri, 15 Aug 1997 00:00:01 GMT<div>J.L. Geluk</div><div>L.F.M. de Haan</div>
The theory of stable probability distributions and their domains of attraction is derived in a direct way (avoiding the usual route via infinitely divisible distributions) using Fourier transforms. Regularly varying functions play an important role in the exposition.On the domain of attraction of exp(-exp(-x))
http://repub.eur.nl/pub/65652/
Mon, 16 Dec 1996 00:00:01 GMT<div>J.L. Geluk</div>
Tails of subordinated laws: The regularly varying case
http://repub.eur.nl/pub/68992/
Mon, 01 Jan 1996 00:00:01 GMT<div>J.L. Geluk</div>