Related papers: Simple Nonlinear Models with Rigorous Extreme Even…
Most extreme events in real life can be faithfully modeled as random realizations from a Generalized Pareto distribution, which depends on two parameters: the scale and the shape. In many actual situations, one is mostly concerned with the…
In general, obtaining the exact steady-state distribution of queue lengths is not feasible. Therefore, we establish bounds for the tail probabilities of queue lengths. Specifically, we examine queueing systems under Heavy-Traffic (HT)…
Causal discovery in multivariate extremes is challenging because extreme observations are sparse, dependent, and often affected by latent common shocks. Existing approaches focus on undirected extremal dependence, require prior graph…
In this paper we consider a stochastic model of perpetuity-type. In contrast to the classical affine perpetuity model of Kesten [12] and Goldie [8] all discount factors in the model are mutually independent. We prove that the tails of the…
We consider a two-node fluid network with batch arrivals of random size having a heavy-tailed distribution. We are interested in the tail asymptotics for the stationary distribution of a two-dimensional queue-length process. The tail…
Causal dependence modelling of multivariate extremes is intended to improve our understanding of the relationships amongst variables associated with rare events. Regular variation provides a standard framework in the study of extremes. This…
The probability and structure of co-occurrences of extreme values in multivariate data may critically depend on auxiliary information provided by covariates. In this contribution, we develop a flexible generalized additive modeling…
This thesis evaluates most of the extreme mixture models and methods that have appended in the literature and implements them in the context of finance and insurance. The paper also reviews and studies extreme value theory, time series,…
Modelling multivariate tail dependence is one of the key challenges in extreme-value theory. Multivariate extremes are usually characterized using parametric models, some of which have simpler submodels at the boundary of their parameter…
We study discrete statistical mechanics systems perturbed by a random environment without a finite second moment. Specifically, we consider a random environment whose tail distribution satisfies $P[\omega > x] \sim x^{-\gamma}$ as $x \to…
This article introduces a non-parametric information-theoretic approach to inference about the tail of a continuous or a discrete distribution. Leveraging a new concept named tail profile -- a set of information-theoretic quantities…
In some fields of applications of stable distributions, especially in economics, it appears, that data have distributions similar to stable in a large region, but do not have such heavy tails. Our aim in this note is to propose several…
The use of expectiles in risk management has recently gathered remarkable momentum due to their excellent axiomatic and probabilistic properties. In particular, the class of elicitable law-invariant coherent risk measures only consists of…
Heavy-tailed probability distributions are extremely useful and play a crucial role in modeling different types of financial data sets. This study presents a two-pronged methodology. First, a mixture probability distribution is created by…
We study the tails of closing auction return distributions for a sample of liquid European stocks. We use the stochastic call auction model of Derksen et al. (2020a), to derive a relation between tail exponents of limit order placement…
We study the probability density function for the fluctuations of the magnetic order parameter in the low temperature phase of the XY model of finite size. In two-dimensions this system is critical over the whole of the low temperature…
Different questions related with analysis of extreme values and outliers arise frequently in practice. To exclude extremal observations and outliers is not a good decision because they contain important information about the observed…
Sums of independent, bounded random variables concentrate around their expectation approximately as well a Gaussian of the same variance. Well known results of this form include the Bernstein, Hoeffding, and Chernoff inequalities and many…
We study the empirical version of halfspace depths with the objective of establishing a connection between the rates of convergence and the tail behaviour of the corresponding underlying distributions. The intricate interplay between the…
This paper investigates the asymptotic behavior of higher-order conditional tail moments, which quantify the contribution of individual losses in the event of systemic collapse. The study is conducted within a framework comprising two…