New copulas based on general partitions-of-unity (part III) — the continuous case

Abstract

In this paper we discuss a natural extension of infinite discrete partition-of-unity copulas which were recently introduced in the literature to continuous partition of copulas with possible applications in risk management and other fields. We present a general simple algorithm to generate such copulas on the basis of the empirical copula from high-dimensional data sets. In particular, our constructions also allow for an implementation of positive tail dependence which sometimes is a desirable property of copula modelling, in particular for internal models under Solvency II.

Adaptive Bernstein Copulas and Risk Management

“…The method of reducing (or, if desired, sharpening) the complexity in the rank structures of the data might also be applied to partition-of-unity copulas (see [24][25][26]). With such copulas, tail dependence can be introduced to the dependence models, which cannot be obtained by Bernstein copulas alone due to the boundedness of the corresponding densities.…”

“…Example 5. Finally, we discuss a high-dimensional data set, which is also analyzed in [24]. It represents economically adjusted windstorm losses in 19 adjacent areas in Central Europe over a time period of 20 years.…”

Wasserstein Dissimilarity for Copula-Based Clustering of Time Series with Spatial Information

“…• a non-parametric approach, which assumes that C ts ij coincides with one smoothed version of the empirical copula associated with the pseudo-observations, such as the empirical checkerboard copula [58,59] or the empirical beta copula [60].…”

Generating unfavourable VaR scenarios under Solvency II with patchwork copulas

“…Patchwork copulas in the context of risk management have been treated in detail by Arbenz et al (2012), Cottin and Pfeifer (2014), Pfeifer (2013), Pfeifer et al (2016Pfeifer et al ( , 2017Pfeifer et al ( , 2019 and Hummel (2018), among others. In several of the cited papers the question of an unfavourable, i.e.…”