Speaker / Predavač : Maddalena Manzi
Title / Naslov: Ultramodularity and a New Construction Method for Copulas
Abstract / Abstrakt:
In this talk we will see that ultramodularity is the simplest way to generalize the axiom of supermodularity for bivariate copulas, because it is stronger than supermodularity and thus it preserves the main axiom for bivariate copulas. We will note that supermodularity is preserved by changing it with ultramodularity, because, instead of rectangles we consider parallelograms. So, in bivariate copulas, we will find new kinds of Archimedean copulas, which deserve special attention because of the convexity of their additive generators and the strong link between ultramodularity and convexity. In the last part, we will see some results obtained with regard to connections between ultramodular Choquet integral-based aggregation functions and their capacity. The talk will be based on some joint works with M. Cardin, M. Kalina, E. P. Klement and R. Mesiar.