Bernoulli and tail-dependence matrices: A simple numerical test

In a recent paper [Embrechts et al., 2015], the question “When is a given matrix [...] the matrix of pairwise (either lower or upper) tail-dependence coefficients?” is investigated and a link to Bernoulli-compatible matrices is provided. This question is interesting, e.g., for model building and stress testing in the financial industry. As part of their conclusions, the authors state that “[...] an interesting open question is how one can (theoretically or numerically) determine whether a given arbitrary non-negative, square matrix is a tail-dependence or Bernoulli-compatible matrix. To the best of our knowledge there are no corresponding algorithms available.” Such an algorithm is provided in this paper and a stochastic model based on its solution is constructed as a corollary. The theoretical foundation of these results stems from [Fiebig et al., 2014], who investigate the geometry of tail-dependence matrices in quite some detail.     «

In a recent paper [Embrechts et al., 2015], the question “When is a given matrix [...] the matrix of pairwise (either lower or upper) tail-dependence coefficients?” is investigated and a link to Bernoulli-compatible matrices is provided. This question is interesting, e.g., for model building and stress testing in the financial industry. As part of their conclusions, the authors state that “[...] an interesting open question is how one can (theoretically or numerically) determine whether a given...     »