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In this paper we study the asymptotic decay of finite time ruin probabilities for an insurance company that faces heavy-tailed claims, uses predictable investment strategies and makes investments in risky assets whose prices evolve…

Risk Management · Quantitative Finance 2008-12-02 Henrik Hult , Filip Lindskog

We derive exponential bounds for tail of distribution for natural, i.e. under ordinary logarithm, normalized sums of arrays of random variables, not necessarily independent.

We offer in this paper the non-asymptotical bilateral sharp exponential estimates for tail of maximum distribution of {\it discontinuous} random fields. Our consideration based on the theory of Prokhorov-Skorokhod spaces of random fields…

Probability · Mathematics 2015-11-02 E. Ostrovsky , L. Sirota

We introduce a trimmed version of the Hill estimator for the index of a heavy-tailed distribution, which is robust to perturbations in the extreme order statistics. In the ideal Pareto setting, the estimator is essentially finite-sample…

Methodology · Statistics 2017-11-15 Shrijita Bhattacharya , Michael Kallitsis , Stilian Stoev

This article discusses modelling of the tail of a multivariate distribution function by means of a large deviation principle (LDP), and its application to the estimation of the probability of a multivariate extreme event from a sample of n…

Statistics Theory · Mathematics 2017-02-23 Cees de Valk

We study deviation of U-statistics when samples have heavy-tailed distribution so the kernel of the U-statistic does not have bounded exponential moments at any positive point. We obtain an exponential upper bound for the tail of the…

Probability · Mathematics 2023-01-30 Milad Bakhshizadeh

Causal questions are omnipresent in many scientific problems. While much progress has been made in the analysis of causal relationships between random variables, these methods are not well suited if the causal mechanisms only manifest…

Methodology · Statistics 2020-09-23 Nicola Gnecco , Nicolai Meinshausen , Jonas Peters , Sebastian Engelke

We study the tail asymptotics of the sum of two heavy-tailed random variables. The dependence structure is modeled by copulas with the so-called tail order property. Examples are presented to illustrate the approach. Further for each…

Risk Management · Quantitative Finance 2024-11-15 Fan Yang , Yi Zhang

In this paper, we investigate the extreme-value methodology, to propose an improved estimator of the conditional tail expectation ($CTE$) for a loss distribution with a finite mean but infinite variance. The present work introduces a new…

Statistics Theory · Mathematics 2020-02-11 Mohamed Laidi , Abdelaziz Rassoul , Hamid Ould Rouis

In this paper we are concerned with a sample of asymptotically independent risks. Tail asymptotic probabilities for linear combinations of randomly weighted order statistics are approximated under various assumptions, where the individual…

Probability · Mathematics 2014-06-24 Alexandru V. Asimit , Enkelejd Hashorva , Dominik Kortschak

We provide some asymptotic theory for the largest eigenvalues of a sample covariance matrix of a p-dimensional time series where the dimension p = p_n converges to infinity when the sample size n increases. We give a short overview of the…

Statistics Theory · Mathematics 2016-04-27 Richard Davis , Johannes Heiny , Thomas Mikosch , Xiaolei Xie

We derive in this article the asymptotic behavior as well as non-asymptotical estimates of tail of distribution for self-normalized sums of random variables (r.v.) under natural classical norming. We investigate also the case of…

Probability · Mathematics 2017-10-10 E. Ostrovsky , L. Sirota

This contribution establishes exact tail asymptotics of $\sup_{(s,t)\in\mathbf{E}}$ $X(s,t)$ for a large class of nonhomogeneous Gaussian random fields $X$ on a bounded convex set $\mathbf{E}\subset\mathbb{R}^2$, with variance function that…

Probability · Mathematics 2016-03-16 Krzysztof Dȩbicki , Enkelejd Hashorva , Lanpeng Ji

We introduce a method to estimate simultaneously the tail and the threshold parameters of an extreme value regression model. This standard model finds its use in finance to assess the effect of market variables on extreme loss distributions…

Methodology · Statistics 2023-04-17 Julien Hambuckers , Marie Kratz , Antoine Usseglio-Carleve

We derive in this short report the exact exponential decreasing tail of distribution for naturel normed sums of independent centered random variables (r.v.), applying the theory of Grand Lebesgue Spaces (GLS). We consider also some…

Probability · Mathematics 2024-09-10 M. R. Formica , E. Ostrovsky , L. Sirota

We consider estimation of the extreme value index and extreme quantiles for heavy-tailed data that are right-censored. We study a general procedure of removing low importance observations in tail estimators. This trimming procedure is…

Statistics Theory · Mathematics 2021-05-13 Martin Bladt , Hansjoerg Albrecher , Jan Beirlant

Modern risk modelling approaches deal with vectors of multiple components. The components could be, for example, returns of financial instruments or losses within an insurance portfolio concerning different lines of business. One of the…

Probability · Mathematics 2021-05-12 Miriam Hägele , Jaakko Lehtomaa

We establish some asymptotic expansions for infinite weighted convolution of distributions having regular varying tails. Various applications to statistics and probability are developed.

Probability · Mathematics 2007-06-13 Ph. Barbe , W. P. McCormick

In this paper, a novel approach to the problem of estimating the heavy-tail exponent alpha>0 of a distribution is proposed. It is based on the fact that block-maxima of size m of the independent and identically distributed data scale at a…

Statistics Theory · Mathematics 2007-06-13 Stilian A. Stoev , George Michailidis , Murad S. Taqqu

This paper introduces a novel measure to quantify the directional dependence of extreme events between two variables. The proposed approach is designed to capture asymmetric tail dependence by studying conditional tail expectations of…

Methodology · Statistics 2026-04-06 Matthieu Garcin , Maxime L. D. Nicolas