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...

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...

This paper provides a new approach to recover relative entropy measures of contemporaneous dependence from limited information by constructing the most entropic copula (MEC) and its canonical form, namely the most entropic canonical copula (MECC). The MECC can effectively be obtained by...

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...

The techniques of exploratory data analysis include a resistant rule, based on a linear combination of quartiles, for identification of outliers. This paper shows that the substitution of the quartiles with the median leads to a better performance in the non-Gaussian case. The improvement occurs...

The contribution of this paper is to derive a bivariate distribution for inflation and output uncertainty with a well-defined role for subjective judgements. The marginal distributions for inflation and output growth are derived from uncertainty in the macro variables that are deemed to be...