In this paper, a characterization of the joint distribution function for the maximum and minimum of a vector is presented in terms of the joint distribution function for the vector. If the joint distribution function is given explicitly, for instance by a copula and marginals, this leads to an...

In terms of regulatory and economic capital, credit risk is the most significant risk faced by banks. We implement a credit risk model - based on publicly available information - with the aim of developing a tool to monitor credit risk in a sample of large and complex banking groups (LCBGs) in...

The Poisson distribution, in general remains sensitive to small departure of frequencies especially at the right tail of the distribution. In many situations it may happen that the Generalized Poisson Distribution (GPD) or a compound distribution provides a closer fit to a frequency distribution...

Stein (1972, 1986) provides a flexible method for measuring the deviation of any probability distribution from a given distribution, thus effectively giving the upper bound of the approximation error which can be represented as the expectation of a Stein's operator. Hosking (1990, 1992) proposes...

In this note we derive closed formulas for the quantiles of a class of cumulative distribution functions (CDF) that can be expressed as mixtures. Generally quantiles of mixtures are only computable numerically. In this case, we assume that the support of the component densities are disjoint,...

Sample covariance is known to be a poor estimate when the data are scarce compared with the dimension. To reduce the estimation error, various structures are usually imposed on the covariance such as low-rank plus diagonal (factor models), banded models and sparse inverse covariances. We...

In practice, multivariate dependencies of extreme risks are often only assessed in a pairwise way. We propose a novel test to detect when bivariate simplifications produce misleading results. This occurs when a significant portion of the multivariate dependence structure in the tails is of...