Related papers: Distributed Inference for Tail Risk

Expected risk minimization (ERM) is at the core of many machine learning systems. This means that the risk inherent in a loss distribution is summarized using a single number - its average. In this paper, we propose a general approach to…

Due to globalization and relaxed market regulation, we have assisted to an increasing of extremal dependence in international markets. As a consequence, several measures of tail dependence have been stated in literature in recent years,…

The distributed Hill estimator is a divide-and-conquer algorithm for estimating the extreme value index when data are stored in multiple machines. In applications, estimates based on the distributed Hill estimator can be sensitive to the…

We establish a statistical learning theoretical framework aimed at extrapolation, or out-of-domain generalization, on the unobserved tails of covariates in continuous regression problems. Our strategy involves performing statistical…

Let $X_{1},\ldots ,X_{n}$ be $n$ real-valued dependent random variables. With motivation from Mitra and Resnick (2009), we derive the tail asymptotic expansion for the weighted sum of order statistics $X_{1:n}\leq \cdots \leq X_{n:n}$ of…

The Generalized Pareto Distribution (GPD) plays a central role in modelling heavy tail phenomena in many applications. Applying the GPD to actual datasets however is a non-trivial task. One common way suggested in the literature to…

We propose an analytical approach to the computation of tail probabilities of compound distributions whose individual components have heavy tails. Our approach is based on the contour integration method, and gives rise to a representation…

A new estimator is proposed for estimating the tail exponent of a heavy-tailed distribution. This estimator, referred to as the layered Hill estimator, is a generalization of the traditional Hill estimator, building upon a layered structure…

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…

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…

We use extreme value theory to estimate the probability of successive exceedances of a threshold value of a time-series of an observable on several classes of chaotic dynamical systems. The observables have either a Fr\'echet (fat-tailed)…

Estimation of tail quantities, such as expected shortfall or Value at Risk, is a difficult problem. We show how the theory of nonlinear expectations, in particular the Data-robust expectation introduced in [5], can assist in the…

Simultaneous occurrences of extreme events need not imply symmetric or reciprocal tail dependence. However, most existing measures of extremal dependence are inherently symmetric and hence often fail to capture directional influence in tail…

In many applied fields, the prediction of more severe events than those already recorded is crucial for safeguarding against potential future calamities. What-if analyses, which evaluate hypothetical scenarios up to the worst-case event,…

Systemic risk measures quantify the potential risk to an individual financial constituent arising from the distress of entire financial system. As a generalization of two widely applied risk measures, Value-at-Risk and Expected Shortfall,…

Extreme events have an important role which is sometime catastrophic in a variety of natural phenomena including climate, earthquakes and turbulence, as well as in man-made environments like financial markets. Statistical analysis and…

In this paper we consider the estimation problem for high quantiles of a heavy-tailed distribution from block data when only a few largest values are observed within blocks. We propose estimators for high quantiles and prove that these…

Conventional methods for extreme event estimation rely on well-chosen parametric models asymptotically justified from extreme value theory (EVT). These methods, while powerful and theoretically grounded, could however encounter a difficult…

We propose an approach to compute the conditional moments of fat-tailed phenomena that, only looking at data, could be mistakenly considered as having infinite mean. This type of problems manifests itself when a random variable Y has a…

The estimation of conditional quantiles at extreme tails is of great interest in numerous applications. Various methods that integrate regression analysis with an extrapolation strategy derived from extreme value theory have been proposed…