Copulas are statistical tools for modelling the multivariate dependence structure among variables in a distribution free way. This paper investigates bivariate copula structure, the existence and uniqueness of bivariate copula decomposition in terms of a comonotonic, an independent, a countermonotonic, and an indecomposable part are proved, while the coefficients are determined by partial deriv...

We present an extension to the Gaussian copula model with jumps. We mix normal distributions which have negative means and small weights with the standard normal distribution in the Gaussian copula model to generate jumps in the default probability distribution for each underlying credit. The means and weights of the new normal distributions are used to control the size and intensity of the jum...

The univariate conditioning of copulas is studied, yielding a construction method for copulas based on an a priori given copula. Based on the gluing method, g-ordinal sum of copulas is introduced and a representation of copulas by means of g-ordinal sums is given. Though different right conditionings commute, this is not the case of right and left conditioning, with a special exception of Archi...

We consider a bottom-up Markovian copula model of portfolio credit risk where instantaneous contagion is possible in the form of simultaneous defaults. Due to the Markovian copula nature of the model, calibration of marginals and dependence parameters can be performed separately using a two-steps procedure, much like in a standard static copula set-up. In this sense this model solves the bottom...

In insurance applications yearly claim totals of different coverage fields are often dependent. In many cases there are numerous claim totals which are zero. A marginal claim distribution will have an additional point mass at zero, hence this probability function will not be continuous at zero and the cumulative distribution functions will not be uniform. Therefore using a copula approach to mo...

In this paper we propose a vine copula based Monte Carlo simulation model for estimating Portfolio Value at Risk. The vine copula model is introduced to analyze the complex dependence structure of different regional markets in the typical financial markets. Then we construct the vine copula based Portfolio Value at Risk model, taking into account the identified high dimensional dependence struc...

The regression function can be expressed in term of copula density and marginal distributions. In this paper, we propose a new method of estimating a regression function using the Bernstein estimator for the copula density and the empirical distributions for the marginal distributions. The method is fully non-parametric and easy to implement. We provide some asymptotic results related to this c...

In insurance applications yearly claim totals of different coverage fields are often dependent. In many cases there are numerous claim totals which are zero. A marginal claim distribution will have an additional point mass at zero, hence this probability function (pf) will not be continuous at zero and the cumulative distribution functions will not be uniform. Therefore using a copula approach ...

This paper presents a new similarity measure based on Rao distance for color texture classification or retrieval. Textures are characterized by a joint model of complex wavelet coefficients. This model is based on a Gaussian Copula in order to consider the dependency between color components. Then, a closed form of Rao distance is computed to measure the difference between two Gaussian Copula b...

In this paper, we propose a method how to construct density weighting functions from Copulas. The notion of Copula was introduced by A. Sklar in 1959. A Copula is a dependence function to construct a bivariate distribution function that links joint distributions to their marginals. Other forms of dependence function, based on density weighing functions, have also been developed. The proposed me...