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We propose a novel probabilistic model to facilitate the learning of multivariate tail dependence of multiple financial assets. Our method allows one to construct from known random vectors, e.g., standard normal, sophisticated joint…

Risk Management · Quantitative Finance 2020-01-14 Xing Yan , Qi Wu , Wen Zhang

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

In this article we show the relationship between the Pareto distribution and the gamma distribution. This shows that the second one, appropriately extended, explains some anomalies that arise in the practical use of extreme value theory.…

Statistics Theory · Mathematics 2012-11-02 Joan del castillo , Jalila Daoudi , Isabel Serra

We tackle the modeling of threshold exceedances in asymptotically independent stochastic processes by constructions based on Laplace random fields. These are defined as Gaussian random fields scaled with a stochastic variable following an…

Methodology · Statistics 2016-03-09 Thomas Opitz

Measures of tail dependence between random variables aim to numerically quantify the degree of association between their extreme realizations. Existing tail dependence coefficients (TDCs) are based on an asymptotic analysis of relevant…

Applications · Statistics 2021-06-11 Davide Lauria , Svetlozar T. Rachev , A. Alexandre Trindade

We study the asymptotic behavior of the marginal expected shortfall when the two random variables are asymptotic independent but positive associated, which is modeled by the so-called tail dependent coefficient. We construct an estimator of…

Statistics Theory · Mathematics 2017-09-14 Juan-Juan Cai , Eni Musta

Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…

Probability · Mathematics 2025-05-27 Robert E. Gaunt , Zixin Ye

We consider multivariate extreme value statistics for independent but nonidentically distributed random vectors. In particular, the data may have varying tail copulas and also heteroscedastic marginal distributions. Assuming smoothly…

Statistics Theory · Mathematics 2026-04-14 John H. J. Einmahl , Chen Zhou

We characterize the second order subexponentiality of an infinitely divisible distribution on the real line under an exponential moment assumption. We investigate the asymptotic behaviour of the difference between the tails of an infinitely…

Probability · Mathematics 2020-01-30 Toshiro Watanabe

The statistical theory of extremes is extended to observations that are non-stationary and not independent. The non-stationarity over time and space is controlled via the scedasis (tail scale) in the marginal distributions. Spatial…

Statistics Theory · Mathematics 2020-03-10 John H. J. Einmahl , Ana Ferreira , Laurens de Haan , Claudia Neves , Chen Zhou

This paper considers the tail asymptotics for a cumulative process $\{B(t); t \ge 0\}$ sampled at a heavy-tailed random time $T$. The main contribution of this paper is to establish several sufficient conditions for the asymptotic equality…

Probability · Mathematics 2013-12-30 Hiroyuki Masuyama

In this paper, we will give a sufficient condition for a non-negative random variable $X$ to be heavy tailed by investigating the Laplace-Stieltjes transform of the probability distribution function. We focus on the relation between the…

Probability · Mathematics 2009-09-02 Kenji Nakagawa

We investigate the differential branching ratio, branching ratio, differential forward-backward asymmetry, the forward-backward asymmetry of the lepton pair and the lepton polarization asymmetry of the exclusive $B\to \tau^+ \tau^- \gamma$…

High Energy Physics - Phenomenology · Physics 2009-11-07 Guray Erkol , Gursevil Turan

We obtain asymptotic approximations for the probability density function of the product of two correlated normal random variables with non-zero means and arbitrary variances. As a consequence, we deduce asymptotic approximations for the…

Probability · Mathematics 2024-10-22 Robert E. Gaunt , Zixin Ye

An asymptotic model for extreme behavior of certain Markov chains is the "tail chain". Generally taking the form of a multiplicative random walk, it is useful in deriving extremal characteristics such as point process limits. We place this…

Probability · Mathematics 2011-12-30 Sidney I. Resnick , David Zeber

Exponential tail bounds for sums play an important role in statistics, but the example of the $t$-statistic shows that the exponential tail decay may be lost when population parameters need to be estimated from the data. However, it turns…

Statistics Theory · Mathematics 2022-03-22 Guenther Walther

Assessing the probability of occurrence of extreme events is a crucial issue in various fields like finance, insurance, telecommunication or environmental sciences. In a multivariate framework, the tail dependence is characterized by the…

Statistics Theory · Mathematics 2015-05-26 Nicolas Goix , Anne Sabourin , Stéphan Clémençon

In many areas of interest, modern risk assessment requires estimation of the extremal behaviour of sums of random variables. We derive the first order upper-tail behaviour of the weighted sum of bivariate random variables under weak…

Statistics Theory · Mathematics 2022-08-17 Jordan Richards , Jonathan A. Tawn

We deal with a discrete-time two-dimensional quasi-birth-and-death process (2d-QBD process for short) on $\mathbb{Z}_+^2\times S_0$, where $S_0$ is a finite set, and give a complete expression for the asymptotic decay function of the…

Probability · Mathematics 2023-02-28 Toshihisa Ozawa

The upper extremes of a Markov chain with regulary varying stationary marginal distribution are known to exhibit under general conditions a multiplicative random walk structure called the tail chain. More generally, if the Markov chain is…

Probability · Mathematics 2007-06-13 Johan Segers