Jef Teugels - Profile on Academia.edu (original) (raw)

Papers by Jef Teugels

We investigate the behavior of some common risk measures for the reinsured amount associated with... more We investigate the behavior of some common risk measures for the reinsured amount associated with a nonproportional reinsurance form defined as a combination of quota-share and drop down excess-of-loss reinsurance treaties. In particular, we consider the Value-at-Risk, the variance, the coefficient of variation, the dispersion and the reduction effect.

Abstract: In this paper we investigate and compare a number of real inversion formulas for the La... more Abstract: In this paper we investigate and compare a number of real inversion formulas for the Laplace transform. The focus is on the accuracy and applicability of the formulas for nu-merical inversion. In this contribution, we study the performance of the formulas for measures concentrated on a positive half-line to continue with measures on an arbitrary half-line.

Statistical Analysis of Catastrophic Events

Lecture Notes in Economics and Mathematical Systems

ABSTRACT We make a first attempt to give an extreme value analysis of data, connected to catastro... more ABSTRACT We make a first attempt to give an extreme value analysis of data, connected to catastrophic events. While the data are readily accessible from SWISSRE, their analysis doesn’t seem to have been taken up. A first set refers to insured claims over the last 35 years; the second deals with victims from natural catastrophes. Together these sets should provide ample proof that extreme value analysis might be able to catch some essential information that traditional statistical analysis might overlook. We finish with a number of cautious remarks.

Why Extreme Value Theory?

Statistics of Extremes

Bayesian Methodology in Extreme Value Statistics

Statistics of Extremes

Let \{X_1, X_2, ...\} be a sequence of independent and identically distributed positive random va... more Let \{X_1, X_2, ...\} be a sequence of independent and identically distributed positive random variables of Pareto-type with index \alpha>0 and let \{N(t); t\geq 0\} be a counting process independent of the X_i's. For any fixed t\geq 0, define T_{N(t)}:=\frac{X_1^2 + X_2^2 + ... + X_{N(t)}^2} {(X_1 + X_2 + ... + X_{N(t)})^2} if N(t)\geq 1 and T_{N(t)}:=0 otherwise. We derive limiting distributions for T_{N(t)} by assuming some convergence properties for the counting process. This is even achieved when both the numerator and the denominator defining T_{N(t)} exhibit an erratic behavior (\mathbb{E}X_1=\infty) or when only the numerator has an erratic behavior (\mathbb{E}X_1<\infty and \mathbb{E}X_1^2=\infty). Thanks to these results, we obtain asymptotic properties pertaining to both the sample coefficient of variation and the sample dispersion.

AFOSR-TR 0-49 6a. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANI... more AFOSR-TR 0-49 6a. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATION ,If applicable) Center for Stochastic Processes 6c ORESS a.

Theory of Probability and Mathematical Statistics

Utilizing Karamata's theory of functions of regular variation, we determine the asymptotic behavi... more Utilizing Karamata's theory of functions of regular variation, we determine the asymptotic behaviour of arbitrary moments E(T k n), k ∈ N, for large n, given that X 1 satisfies a tail condition, akin to the domain of attraction condition from extreme value theory. As a by-product, the paper offers a new method for estimating the extreme value index of Pareto-type tails.

Asymptotics of Hill’s estimator

Etude du probleme du domaine d'attraction de l'estimateur de Hill introduit comme un esti... more Etude du probleme du domaine d'attraction de l'estimateur de Hill introduit comme un estimateur du maximum de vraisemblance pour la queue d'une distribution. Extension des conditions de normalite asymptotique

This vignette uses the evd package to reproduce the figures, tables and analysis in Chapter 9 of ... more This vignette uses the evd package to reproduce the figures, tables and analysis in Chapter 9 of Beirlant et al. (2001). The chapter was written by Segers and Vandewalle (2004). The code reproduces almost all figures, but for space reasons only some are shown. Deviations from the book are given as footnotes. Differences will inevitably exist due to numerical optimization and random number generation.

Multivariate Extreme Value Theory

Theory of Probability and Mathematical Statistics, 2007

Utilizing Karamata's theory of functions of regular variation, we determine the asymptotic behavi... more Utilizing Karamata's theory of functions of regular variation, we determine the asymptotic behaviour of arbitrary moments E(T k n), k ∈ N, for large n, given that X 1 satisfies a tail condition, akin to the domain of attraction condition from extreme value theory. As a by-product, the paper offers a new method for estimating the extreme value index of Pareto-type tails.

AFOSR-TR 0-49 6a. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANI... more AFOSR-TR 0-49 6a. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATION ,If applicable) Center for Stochastic Processes 6c ORESS a.

The Probabilistic Side of Extreme Value Theory

Tail Estimation for All Domains of Attraction

Tail Estimation under Pareto‐Type Models

On the Rate of Convergence in Renewal and Markov Renewal Processes

We investigate the behavior of some common risk measures for the reinsured amount associated with... more We investigate the behavior of some common risk measures for the reinsured amount associated with a nonproportional reinsurance form defined as a combination of quota-share and drop down excess-of-loss reinsurance treaties. In particular, we consider the Value-at-Risk, the variance, the coefficient of variation, the dispersion and the reduction effect.

Abstract: In this paper we investigate and compare a number of real inversion formulas for the La... more Abstract: In this paper we investigate and compare a number of real inversion formulas for the Laplace transform. The focus is on the accuracy and applicability of the formulas for nu-merical inversion. In this contribution, we study the performance of the formulas for measures concentrated on a positive half-line to continue with measures on an arbitrary half-line.

Statistical Analysis of Catastrophic Events

Lecture Notes in Economics and Mathematical Systems

ABSTRACT We make a first attempt to give an extreme value analysis of data, connected to catastro... more ABSTRACT We make a first attempt to give an extreme value analysis of data, connected to catastrophic events. While the data are readily accessible from SWISSRE, their analysis doesn’t seem to have been taken up. A first set refers to insured claims over the last 35 years; the second deals with victims from natural catastrophes. Together these sets should provide ample proof that extreme value analysis might be able to catch some essential information that traditional statistical analysis might overlook. We finish with a number of cautious remarks.

Why Extreme Value Theory?

Statistics of Extremes

Bayesian Methodology in Extreme Value Statistics

Statistics of Extremes

Let \{X_1, X_2, ...\} be a sequence of independent and identically distributed positive random va... more Let \{X_1, X_2, ...\} be a sequence of independent and identically distributed positive random variables of Pareto-type with index \alpha>0 and let \{N(t); t\geq 0\} be a counting process independent of the X_i's. For any fixed t\geq 0, define T_{N(t)}:=\frac{X_1^2 + X_2^2 + ... + X_{N(t)}^2} {(X_1 + X_2 + ... + X_{N(t)})^2} if N(t)\geq 1 and T_{N(t)}:=0 otherwise. We derive limiting distributions for T_{N(t)} by assuming some convergence properties for the counting process. This is even achieved when both the numerator and the denominator defining T_{N(t)} exhibit an erratic behavior (\mathbb{E}X_1=\infty) or when only the numerator has an erratic behavior (\mathbb{E}X_1<\infty and \mathbb{E}X_1^2=\infty). Thanks to these results, we obtain asymptotic properties pertaining to both the sample coefficient of variation and the sample dispersion.

AFOSR-TR 0-49 6a. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANI... more AFOSR-TR 0-49 6a. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATION ,If applicable) Center for Stochastic Processes 6c ORESS a.

Theory of Probability and Mathematical Statistics

Utilizing Karamata's theory of functions of regular variation, we determine the asymptotic behavi... more Utilizing Karamata's theory of functions of regular variation, we determine the asymptotic behaviour of arbitrary moments E(T k n), k ∈ N, for large n, given that X 1 satisfies a tail condition, akin to the domain of attraction condition from extreme value theory. As a by-product, the paper offers a new method for estimating the extreme value index of Pareto-type tails.

Asymptotics of Hill’s estimator

Etude du probleme du domaine d'attraction de l'estimateur de Hill introduit comme un esti... more Etude du probleme du domaine d'attraction de l'estimateur de Hill introduit comme un estimateur du maximum de vraisemblance pour la queue d'une distribution. Extension des conditions de normalite asymptotique

This vignette uses the evd package to reproduce the figures, tables and analysis in Chapter 9 of ... more This vignette uses the evd package to reproduce the figures, tables and analysis in Chapter 9 of Beirlant et al. (2001). The chapter was written by Segers and Vandewalle (2004). The code reproduces almost all figures, but for space reasons only some are shown. Deviations from the book are given as footnotes. Differences will inevitably exist due to numerical optimization and random number generation.

Multivariate Extreme Value Theory

Theory of Probability and Mathematical Statistics, 2007

Utilizing Karamata's theory of functions of regular variation, we determine the asymptotic behavi... more Utilizing Karamata's theory of functions of regular variation, we determine the asymptotic behaviour of arbitrary moments E(T k n), k ∈ N, for large n, given that X 1 satisfies a tail condition, akin to the domain of attraction condition from extreme value theory. As a by-product, the paper offers a new method for estimating the extreme value index of Pareto-type tails.

AFOSR-TR 0-49 6a. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANI... more AFOSR-TR 0-49 6a. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATION ,If applicable) Center for Stochastic Processes 6c ORESS a.

The Probabilistic Side of Extreme Value Theory

Tail Estimation for All Domains of Attraction

Tail Estimation under Pareto‐Type Models

On the Rate of Convergence in Renewal and Markov Renewal Processes