Related papers: Combined Tail Estimation Using Censored Data and E…

Classical Monte Carlo methods for pricing catastrophe insurance tail risk converge at order reciprocal root N, requiring large simulation budgets to resolve upper-tail percentiles of the loss distribution. This sample-sparsity problem can…

For a risk vector $V$, whose components are shared among agents by some random mechanism, we obtain asymptotic lower and upper bounds for the individual agents' exposure risk and the aggregated risk in the market. Risk is measured by…

The task of analyzing extreme events with censoring effects is considered under a framework allowing for random covariate information. A wide class of estimators that can be cast as product-limit integrals is considered, for when the…

Gini-type correlation coefficients have become increasingly important in a variety of research areas, including economics, insurance and finance, where modelling with heavy-tailed distributions is of pivotal importance. In such situations,…

This paper studies the quantization of heavy-tailed data in some fundamental statistical estimation problems, where the underlying distributions have bounded moments of some order. We propose to truncate and properly dither the data prior…

Given an arbitrary continuous probability density function, it is introduced a conjugated probability density, which is defined through the Shannon information associated with its cumulative distribution function. These new densities are…

We consider quantile regression processes from censored data under dependent data structures and derive a uniform Bahadur representation for those processes. We also consider cases where the dimension of the parameter in the quantile…

Recently, the concept of tail dependence has been discussed in financial applications related to market or credit risk. The multivariate extreme value theory is a proper tool to measure and model dependence, for example, of large loss…

Copula modeling has gained much attention in many fields recently with the advantage of separating dependence structure from marginal distributions. In real data, however, serious ties are often present in one or multiple margins, which…

For extreme value estimation we propose to use a model with a Dirichlet process mixture of gamma densities in the center and generalized Pareto densities for the tails. Due to the randomness in the center and a heavy tailed density in the…

We propose an $\ell_1$-penalized estimator for high-dimensional models of Expected Shortfall (ES). The estimator is obtained as the solution to a least-squares problem for an auxiliary dependent variable, which is defined as a…

A novel forecast combination and weighted quantile based tail-risk forecasting framework is proposed, aiming to reduce the impact of modelling uncertainty in tail-risk forecasting. The proposed approach is based on a two-step estimation…

The central limit theorem introduced by Stute [The central limit theorem under random censorship. Ann. Statist. 1995; 23: 422-439] does not hold for some class of heavy-tailed distributions. In this paper, we make use of the extreme value…

The existence of large and extreme claims of a non-life insurance portfolio influences the ability of (re)insurers to estimate the reserve. The excess over-threshold method provides a way to capture and model the typical behaviour of…

A theoretical expression is derived for the mean squared error of a nonparametric estimator of the tail dependence coefficient, depending on a threshold that defines which rank delimits the tails of a distribution. We propose a new method…

In recent years several attempts have been made to extend tail modelling towards the modal part of the data. Frigessi et al. (2002) introduced dynamic mixtures of two components with a weight function {\pi} = {\pi}(x) smoothly connecting…

A wide range of natural and social phenomena result in observables whose distributions can be well approximated by a power-law decay. The well-known Hill estimator of the tail exponent provides results which are in many respects superior to…

Analysing dependent risks is an important task for insurance companies. A dependency is reflected in the fact that information about one random variable provides information about the likely distribution of values of another random…

For the estimation of cumulative link models for ordinal data, the bias-reducing adjusted score equations in \citet{firth:93} are obtained, whose solution ensures an estimator with smaller asymptotic bias than the maximum likelihood…

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…