Some multivariate imprecise shock model copulas

TL;DR

This paper explores the extension of imprecise copulas to multivariate shock models, developing theoretical foundations and properties for different classes, including the first theory of bivariate imprecise RMM copulas.

Contribution

It introduces the first multivariate imprecise shock model copulas, develops their properties, and initiates a new theoretical framework for this class of models.

Findings

Coherent sets of distributions and copulas in Marshall's case.

Properties of maxmin and reflected maxmin (RMM) imprecise copulas.

Unfolded the theory of bivariate imprecise RMM copulas.

Abstract

Bivariate imprecise copulas have recently attracted substantial attention. However, the multivariate case seems still to be a "blank slate". It is then natural that this idea be tested first on shock model induced copulas, a family which might be the most useful in various applications. We investigate a model in which some of the shocks are assumed imprecise and develop the corresponding set of copulas. In the Marshall's case we get a coherent set of distributions and a coherent set of copulas, where the bounds are naturally corresponding to each other. The situation with the other two groups of multivariate imprecise shock model induced copulas, i.e., the maxmin and the the reflected maxmin (RMM) copulas, is substantially more involved, but we are still able to produce their properties. These are the main results of the paper that serves as the first step into a theory that should develop in this direction. In addition, we unfold the theory of bivariate imprecise RMM copulas that has not yet been done before.