Related papers: Sharp large deviation estimates for heavy-tailed e…
Insurance data can be asymmetric with heavy tails, causing inadequate adjustments of the usually applied models. To deal with this issue, hierarchical models for collective risk with heavy-tails of the claims distributions that take also…
Several novel statistical methods have been developed to estimate large integrated volatility matrices based on high-frequency financial data. To investigate their asymptotic behaviors, they require a sub-Gaussian or finite high-order…
In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable $V$ satisfying the distributional equation $V\stackrel{\mathcal{D}}{=}f(V)$,…
Motivated by the prominence of Conditional Value-at-Risk (CVaR) as a measure for tail risk in settings affected by uncertainty, we develop a new formula for approximating CVaR based optimization objectives and their gradients from limited…
This article studies asymptotic approximations of ruin probabilities of multivariate random walks with heavy-tailed increments. Under our assumptions, the distributions of the increments are closely connected to multivariate…
We present sharp tail asymptotics for the density and the distribution function of linear combinations of correlated log-normal random variables, that is, exponentials of components of a correlated Gaussian vector. The asymptotic behavior…
In this work, we provide robust bounds on the tail probabilities and the tail index of heavy-tailed distributions in the context of model misspecification. They are defined as the optimal value when computing the worst-case tail behavior…
It is well-known that large deviations of random walks driven by independent and identically distributed heavy-tailed random variables are governed by the so-called principle of one large jump. We note that further subtleties hold for such…
We develop an unsupervised mixture model for non-negative, skewed and heavy-tailed data, such as losses in actuarial and risk management applications. The mixture has a lognormal component, which is usually appropriate for the body of the…
Statistical analysis of extremes can be used to predict the probability of future extreme events, such as large rainfalls or devastating windstorms. The quality of these forecasts can be measured through scoring rules. Locally scale…
In this paper we develop a novel inferential approach based on geometric records for estimating the tail index of heavy-tailed distributions. We construct a maximum likelihood estimator for the Pareto model and establish its strong…
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)…
Let $\{X_1, X_2, ... \}$ be a sequence of dependent heavy-tailed random variables with distributions $F_1, F_2,...$ on $(-\infty,\infty)$, and let $\tau$ be a nonnegative integer-valued random variable independent of the sequence $\{X_k, k…
We characterize the complex, heavy-tailed probability distribution functions (pdf) describing the response and its local extrema for structural systems subjected to random forcing that includes extreme events. Our approach is based on the…
We study tail risk dynamics in high-frequency financial markets and their connection with trading activity and market uncertainty. We introduce a dynamic extreme value regression model accommodating both stationary and local unit-root…
Let $\eta_1$, $\eta_2,\ldots$ be independent copies of a random variable $\eta$ with zero mean and finite variance which is bounded from the right, that is, $\eta\leq b$ almost surely for some $b>0$. Considering different types of the…
We provide large deviations estimates for the upper tail of the number of triangles in scale-free inhomogeneous random graphs where the degrees have power law tails with index $-\alpha, \alpha \in (1,2)$. We show that upper tail…
For purposes of Value-at-Risk estimation, we consider several multivariate families of heavy-tailed distributions, which can be seen as multidimensional versions of Paretian stable and Student's t distributions allowing different marginals…
The subject of tail estimation for randomly censored data from a heavy tailed distribution receives growing attention, motivated by applications for instance in actuarial statistics. The bias of the available estimators of the extreme value…
The non-asymptotic tail bounds of random variables play crucial roles in probability, statistics, and machine learning. Despite much success in developing upper bounds on tail probability in literature, the lower bounds on tail…