Related papers: Tail Asymptotics of Deflated Risks

We obtain decay rates of probabilities of tails of polynomials in several independent random variables with heavy tails and derive stable limit theorems for nonconventional sums of such polynomials

Value at risk (VaR) and expected shortfall (ES) are common high quantile-based risk measures adopted in financial regulations and risk management. In this paper, we propose a tail risk measure based on the most probable maximum size of risk…

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…

The joint Value at Risk (VaR) and expected shortfall (ES) quantile regression model of Taylor (2017) is extended via incorporating a realized measure, to drive the tail risk dynamics, as a potentially more efficient driver than daily…

We introduce a statistical model for operational losses based on heavy-tailed distributions and bipartite graphs, which captures the event type and business line structure of operational risk data. The model explicitly takes into account…

In this paper, we study the asymptotic behavior of the tail probability of the number of customers in the steady-state $M/G/1$ retrial queue with Bernoulli schedule, under the assumption that the service time distribution has a regularly…

Considerable literature has been devoted to developing statistical inferential results for risk measures, especially for those that are of the form of L-functionals. However, practical and theoretical considerations have highlighted quite a…

We prove tail estimates for variables $\sum_i f(X_i)$, where $(X_i)_i$ is the trajectory of a random walk on an undirected graph (or, equivalently, a reversible Markov chain). The estimates are in terms of the maximum of the function $f$,…

We introduce a new functional measure of tail dependence for weakly dependent (asymptotically independent) random vectors, termed weak tail dependence function. The new measure is defined at the level of copulas and we compute it for…

In recent years research on credit risk modelling has mainly focused on default probabilities. Recovery rates are usually modelled independently, quite often they are even assumed constant. Then, however, the structural connection between…

In this paper, we investigate risk measures such as value at risk (VaR) and the conditional tail expectation (CTE) of the extreme (maximum and minimum) and the aggregate (total) of two dependent risks. In finance, insurance and the other…

Correlation mixtures of elliptical copulas arise when the correlation parameter is driven itself by a latent random process. For such copulas, both penultimate and asymptotic tail dependence are much larger than for ordinary elliptical…

The paper presents an efficient method for simulating the tails of a target variable Z=h(X) which depends on a set of basic variables X=(X_1, ..., X_n). To this aim, variables X_i, i=1, ..., n are sequentially simulated in such a manner…

We study the asymptotic tail probability of the first-passage time over a moving boundary for a random walk conditioned to return to zero, where the increments of the random walk have finite variance. Typically, the asymptotic tail behavior…

Hidden regular variation is a sub-model of multivariate regular variation and facilitates accurate estimation of joint tail probabilities. We generalize the model of hidden regular variation to what we call hidden domain of attraction. We…

Inflation exhibits state-dependent, skewed, and fat-tailed dynamics that make risk a central concern for monetary policy. Accordingly, inflation risks are distributional and cannot be fully captured by mean-based models. We propose a…

We take an $L_1$-dense class of functions $\Cal F$ on a measurable space $(X,\Cal X)$ and a sequence of i.i.d. $X$-valued random variables $\xi_1,\dots,\xi_n$, and give a good estimate on the tail behaviour of $\sup\limits_{f\in\Cal…

We consider the estimation of small probabilities or other risk quantities associated with rare but catastrophic events. In the model-based literature, much of the focus has been devoted to efficient Monte Carlo computation or analytical…

We present a new family of estimators of the Weibull tail-coefficient. The Weibull tail-coefficient is defined as the regular variation coefficient of the inverse failure rate function. Our estimators are based on a linear combination of…

The relationship between a response variable and its covariates can vary significantly, especially in scenarios where covariates take on extremely high or low values. This paper introduces a max-linear tail regression model specifically…