Related papers: Hidden regular variation, copula models, and the l…
This article extends the literature on copulas with discrete or continuous marginals to the case where some of the marginals are a mixture of discrete and continuous components. We do so by carefully defining the likelihood as the density…
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…
Tuning parameters are parameters involved in an estimating procedure for the purpose of reducing the risk of some other estimator. Examples include the degree of penalization in penalized regression and likelihood problems, as well as the…
A time-varying bivariate copula joint model, which models the repeatedly measured longitudinal outcome at each time point and the survival data jointly by both the random effects and time-varying bivariate copulas, is proposed in this…
Given two multivariate copulas with corresponding tail dependence functions, we investigate the relation between a natural tail dependence ordering $\leq_{tdo}$ and the order $\leq_{loc}$ of local stochastic dominance. We show that,…
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…
The continuous extension of a discrete random variable is amongst the computational methods used for estimation of multivariate normal copula-based models with discrete margins. Its advantage is that the likelihood can be derived…
This paper studies properties of functions having monotone tails. We extend Theorem 1 of Dhaene et al. (2002a) and show how the tail quantiles of a random variable transformed with a monotone tail function can be expressed as the…
We discuss the connection between information and copula theories by showing that a copula can be employed to decompose the information content of a multivariate distribution into marginal and dependence components, with the latter…
We propose a copula-based extension of the hidden Markov model (HMM) which applies when the observations recorded at each time in the sample are multivariate. The joint model produced by the copula extension allows decoding of the hidden…
We investigate the relative information content of six measures of dependence between two random variables $X$ and $Y$ for large or extreme events for several models of interest for financial time series. The six measures of dependence are…
Distortion risk measures are extensively used in finance and insurance applications because of their appealing properties. We present three methods to construct new class of distortion functions and measures. The approach involves the…
We propose a multivariate generative model to capture the complex dependence structure often encountered in business and financial data. Our model features heterogeneous and asymmetric tail dependence between all pairs of individual…
Based on suitable left-truncated or censored data, two flexible classes of $M$-estimations of Weibull tail coefficient are proposed with two additional parameters bounding the impact of extreme contamination. Asymptotic normality with…
In risk management, tail risks are of crucial importance. The assessment of risks should be carried out in accordance with the regulatory authority's requirement at high quantiles. In general, the underlying distribution function is…
In situations where both extreme and non-extreme data are of interest, modelling the whole data set accurately is important. In a univariate framework, modelling the bulk and tail of a distribution has been extensively studied before.…
This article discusses modelling of the tail of a multivariate distribution function by means of a large deviation principle (LDP), and its application to the estimation of the probability of a multivariate extreme event from a sample of n…
We study dynamic risk measures in a very general framework enabling to model uncertainty and processes with jumps. We previously showed the existence of a canonical equivalence class of probability measures hidden behind a given set of…
As a motivating problem, we aim to study some special aspects of the marginal distributions of the order statistics for exchangeable and (more generally) for minimally stable non-negative random variables $T_{1},...,T_{r}$. In any case, we…
We address the problem that classical risk measures may not detect the tail risk adequately. This can occur for instance due to averaging when calculating the Expected Shortfall. The current literature proposes the so-called adjusted…